Podcast
Questions and Answers
What is the value of 𝑡𝑎𝑛(45°−α) (𝑐𝑜𝑠19°+𝑠𝑖𝑛71°)(𝑠𝑒𝑐19°+𝑐𝑜𝑠𝑒𝑐71°) / 𝑐𝑜𝑡(45°+α)?
What is the value of 𝑡𝑎𝑛(45°−α) (𝑐𝑜𝑠19°+𝑠𝑖𝑛71°)(𝑠𝑒𝑐19°+𝑐𝑜𝑠𝑒𝑐71°) / 𝑐𝑜𝑡(45°+α)?
What is the value of sin28°sin35°sin45°sec62°sec55°?
What is the value of sin28°sin35°sin45°sec62°sec55°?
What is the value of (𝑐𝑜𝑠9°+𝑠𝑖𝑛81°)(𝑠𝑒𝑐9°+𝑐𝑜𝑠𝑒𝑐81°)?
What is the value of (𝑐𝑜𝑠9°+𝑠𝑖𝑛81°)(𝑠𝑒𝑐9°+𝑐𝑜𝑠𝑒𝑐81°)?
What is the value of 𝑐𝑜𝑠𝑒𝑐 71°+𝑐𝑜𝑠 15°−𝑡𝑎𝑛 19°+𝑐𝑜𝑠 75°?
What is the value of 𝑐𝑜𝑠𝑒𝑐 71°+𝑐𝑜𝑠 15°−𝑡𝑎𝑛 19°+𝑐𝑜𝑠 75°?
Signup and view all the answers
What is the value of 𝑡𝑎𝑛12°𝑡𝑎𝑛24°𝑡𝑎𝑛66°𝑡𝑎𝑛78°?
What is the value of 𝑡𝑎𝑛12°𝑡𝑎𝑛24°𝑡𝑎𝑛66°𝑡𝑎𝑛78°?
Signup and view all the answers
What is the value of 𝑡𝑎𝑛(45°−α) (𝑐𝑜𝑠19°+𝑠𝑖𝑛71°)(𝑠𝑒𝑐19°+𝑐𝑜𝑠𝑒𝑐71°) / 𝑐𝑜𝑡(45°+α)?
What is the value of 𝑡𝑎𝑛(45°−α) (𝑐𝑜𝑠19°+𝑠𝑖𝑛71°)(𝑠𝑒𝑐19°+𝑐𝑜𝑠𝑒𝑐71°) / 𝑐𝑜𝑡(45°+α)?
Signup and view all the answers
What is the value of 𝑐𝑜𝑡(45°+α)?
What is the value of 𝑐𝑜𝑡(45°+α)?
Signup and view all the answers
What is the value of sin28°sin35°sin45°?
What is the value of sin28°sin35°sin45°?
Signup and view all the answers
What is the value of 3cosθ – 4cos³θ if sinθ = 1/2?
What is the value of 3cosθ – 4cos³θ if sinθ = 1/2?
Signup and view all the answers
If tan40° = α, what is the value of tan320° – tan310° 1+tan320°.tan310°?
If tan40° = α, what is the value of tan320° – tan310° 1+tan320°.tan310°?
Signup and view all the answers
What is the value of 8sin30°sin60° - 4sin90° - sec45°?
What is the value of 8sin30°sin60° - 4sin90° - sec45°?
Signup and view all the answers
If sinθ = 1/2, what is the value of cosθ?
If sinθ = 1/2, what is the value of cosθ?
Signup and view all the answers
What is the value of tan320° - tan310°?
What is the value of tan320° - tan310°?
Signup and view all the answers
If tan40° = α, what is the value of 1+α²?
If tan40° = α, what is the value of 1+α²?
Signup and view all the answers
What is the value of sinθ if 3cosθ – 4cos³θ = 0?
What is the value of sinθ if 3cosθ – 4cos³θ = 0?
Signup and view all the answers
What is the value of sec45°?
What is the value of sec45°?
Signup and view all the answers
What is the value of 2sin4θ + sin²θ if cot²θ + cot4θ = 2?
What is the value of 2sin4θ + sin²θ if cot²θ + cot4θ = 2?
Signup and view all the answers
If tanθ + 3cotθ - 2√3 = 0, what is the value of cosec²θ + cos²θ?
If tanθ + 3cotθ - 2√3 = 0, what is the value of cosec²θ + cos²θ?
Signup and view all the answers
What is the value of k if k - k cot 30° = sin²60° + 4tan²45° - 1/cot 30°?
What is the value of k if k - k cot 30° = sin²60° + 4tan²45° - 1/cot 30°?
Signup and view all the answers
What is the value of cot²θ + cot4θ if 2sin4θ + sin²θ = 2?
What is the value of cot²θ + cot4θ if 2sin4θ + sin²θ = 2?
Signup and view all the answers
If cot²θ + cot4θ = 2, what is the value of sin²θ?
If cot²θ + cot4θ = 2, what is the value of sin²θ?
Signup and view all the answers
What is the value of tanθ if tanθ + 3cotθ - 2√3 = 0?
What is the value of tanθ if tanθ + 3cotθ - 2√3 = 0?
Signup and view all the answers
What is the value of cosec²60° + 4tan²45° - 1/cot 30°?
What is the value of cosec²60° + 4tan²45° - 1/cot 30°?
Signup and view all the answers
If k - k cot 30° = sin²60° + 4tan²45° - 1/cot 30°, what is the value of k - 1?
If k - k cot 30° = sin²60° + 4tan²45° - 1/cot 30°, what is the value of k - 1?
Signup and view all the answers
What is the value of $\frac{sec\theta + cos\sec^2\theta}{sin\theta(1+cos\theta)} \times \frac{1+cos\theta-sin^2\theta}{1}$, where $0° < θ < 90°$?
What is the value of $\frac{sec\theta + cos\sec^2\theta}{sin\theta(1+cos\theta)} \times \frac{1+cos\theta-sin^2\theta}{1}$, where $0° < θ < 90°$?
Signup and view all the answers
What is the value of $\frac{2sec\theta + cos\sec^2\theta}{sin\theta(1+cos\theta)} \times \frac{1+cos\theta-sin^2\theta}{1}$, where $0° < θ < 90°$?
What is the value of $\frac{2sec\theta + cos\sec^2\theta}{sin\theta(1+cos\theta)} \times \frac{1+cos\theta-sin^2\theta}{1}$, where $0° < θ < 90°$?
Signup and view all the answers
Which trigonometric function is equal to $\frac{1+cos\theta-sin^2\theta}{sin\theta(1+cos\theta)}$?
Which trigonometric function is equal to $\frac{1+cos\theta-sin^2\theta}{sin\theta(1+cos\theta)}$?
Signup and view all the answers
What is the value of $\frac{2}{1+cos\theta-sin^2\theta}$, where $0° < θ < 90°$?
What is the value of $\frac{2}{1+cos\theta-sin^2\theta}$, where $0° < θ < 90°$?
Signup and view all the answers
What is the value of $\frac{1}{sin\theta(1+cos\theta)}$, where $0° < θ < 90°$?
What is the value of $\frac{1}{sin\theta(1+cos\theta)}$, where $0° < θ < 90°$?
Signup and view all the answers
What is the value of $\frac{1+cos\theta-sin^2\theta}{sin\theta}$, where $0° < θ < 90°$?
What is the value of $\frac{1+cos\theta-sin^2\theta}{sin\theta}$, where $0° < θ < 90°$?
Signup and view all the answers
What is the value of $\frac{sec\theta + cos\sec^2\theta}{1+cos\theta-sin^2\theta}$, where $0° < θ < 90°$?
What is the value of $\frac{sec\theta + cos\sec^2\theta}{1+cos\theta-sin^2\theta}$, where $0° < θ < 90°$?
Signup and view all the answers
What is the value of $\frac{sin\theta(1+cos\theta)}{1+cos\theta-sin^2\theta}$, where $0° < θ < 90°$?
What is the value of $\frac{sin\theta(1+cos\theta)}{1+cos\theta-sin^2\theta}$, where $0° < θ < 90°$?
Signup and view all the answers
What is the value of 2cotθ - 3cosθ?
What is the value of 2cotθ - 3cosθ?
Signup and view all the answers
What is the value of 3secθ + tanθ when θ lies in the first quadrant?
What is the value of 3secθ + tanθ when θ lies in the first quadrant?
Signup and view all the answers
What is the value of 3cot47° - sec43° - 2(tan23° - cosec67°)?
What is the value of 3cot47° - sec43° - 2(tan23° - cosec67°)?
Signup and view all the answers
What is the value of cosec(68° + θ) - tan(θ + 61°) - tan(22° - θ) + cot(29° - θ)?
What is the value of cosec(68° + θ) - tan(θ + 61°) - tan(22° - θ) + cot(29° - θ)?
Signup and view all the answers
What is the equation given in the problem?
What is the equation given in the problem?
Signup and view all the answers
What is the quadrant in which θ lies?
What is the quadrant in which θ lies?
Signup and view all the answers
What is the value of 2(cotθ - 3cosθ) / (3cotθ - secθ)?
What is the value of 2(cotθ - 3cosθ) / (3cotθ - secθ)?
Signup and view all the answers
What is the value of secθ + tanθ when θ lies in the first quadrant?
What is the value of secθ + tanθ when θ lies in the first quadrant?
Signup and view all the answers
Study Notes
Trigonometry Formulas and Identities
- If sinθ = 1/2, then the value of (3cosθ – 4cos³θ) is 0.
Trigonometric Ratios and Identities
- tan40° = α, then (tan320° - tan310°) / (1 + tan320°.tan310°) = α² / (1 - α²).
- cot²θ + cot⁴θ = 2, then 2sin⁴θ + sin²θ = 3.
Trigonometric Identities and Formulas
- sin28°sin35°sin45°sec62°sec55° = -2.
- sin(A + B) = sinAcosB + cosAsinB (used to find the value of sin28°sin35°sin45°sec62°sec55°).
- tan(A - B) = (tanA - tanB) / (1 + tanAtanB) (used to find the value of tan40°).
Trigonometric Formulas and Inequalities
- 2sin4θ + sin²θ = 3, if cot²θ + cot⁴θ = 2.
- |tanθ| ≥ |tan(45° - α)| (used to find the value of 2sin4θ + sin²θ).
Trigonometry Applications and Formulas
- 8sin30°sin60° - 4sin90° - sec45° = 2.
- tan(45° - α) / (cot45° + sec45°) = tan(45° + α) (used to find the value of 8sin30°sin60° - 4sin90° - sec45°).
Trigonometric Identities and Formulas
- (cosec²θ + cos²θ) = 2, if tanθ + 3cotθ - 2√3 = 0, 0° < θ < 90°.
- sec²θ - tan²θ = 1 (used to find the value of cosec²θ + cos²θ).
Trigonometry Formulas and Identities
- 2sin⁴θ + sin²θ = 5, if 7sinθ + 4cosθ = 5 and θ lies in the first quadrant.
- 3secθ + tanθ = 5, if 7sinθ + 4cosθ = 5 and θ lies in the first quadrant.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
