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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)?
- -1
- 0 (correct)
- 2
- 1
What is the value of sin28°sin35°sin45°sec62°sec55°?
What is the value of sin28°sin35°sin45°sec62°sec55°?
- 0
- 2
- -2
- -3 (correct)
What is the value of (𝑐𝑜𝑠9°+𝑠𝑖𝑛81°)(𝑠𝑒𝑐9°+𝑐𝑜𝑠𝑒𝑐81°)?
What is the value of (𝑐𝑜𝑠9°+𝑠𝑖𝑛81°)(𝑠𝑒𝑐9°+𝑐𝑜𝑠𝑒𝑐81°)?
- 1 (correct)
- 2
- 0
- -1
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°?
What is the value of 𝑡𝑎𝑛12°𝑡𝑎𝑛24°𝑡𝑎𝑛66°𝑡𝑎𝑛78°?
What is the value of 𝑡𝑎𝑛12°𝑡𝑎𝑛24°𝑡𝑎𝑛66°𝑡𝑎𝑛78°?
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 𝑐𝑜𝑡(45°+α)?
What is the value of 𝑐𝑜𝑡(45°+α)?
What is the value of sin28°sin35°sin45°?
What is the value of sin28°sin35°sin45°?
What is the value of 3cosθ – 4cos³θ if sinθ = 1/2?
What is the value of 3cosθ – 4cos³θ if sinθ = 1/2?
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°?
What is the value of 8sin30°sin60° - 4sin90° - sec45°?
What is the value of 8sin30°sin60° - 4sin90° - sec45°?
If sinθ = 1/2, what is the value of cosθ?
If sinθ = 1/2, what is the value of cosθ?
What is the value of tan320° - tan310°?
What is the value of tan320° - tan310°?
If tan40° = α, what is the value of 1+α²?
If tan40° = α, what is the value of 1+α²?
What is the value of sinθ if 3cosθ – 4cos³θ = 0?
What is the value of sinθ if 3cosθ – 4cos³θ = 0?
What is the value of sec45°?
What is the value of sec45°?
What is the value of 2sin4θ + sin²θ if cot²θ + cot4θ = 2?
What is the value of 2sin4θ + sin²θ if cot²θ + cot4θ = 2?
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?
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°?
What is the value of cot²θ + cot4θ if 2sin4θ + sin²θ = 2?
What is the value of cot²θ + cot4θ if 2sin4θ + sin²θ = 2?
If cot²θ + cot4θ = 2, what is the value of sin²θ?
If cot²θ + cot4θ = 2, what is the value of sin²θ?
What is the value of tanθ if tanθ + 3cotθ - 2√3 = 0?
What is the value of tanθ if tanθ + 3cotθ - 2√3 = 0?
What is the value of cosec²60° + 4tan²45° - 1/cot 30°?
What is the value of cosec²60° + 4tan²45° - 1/cot 30°?
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?
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 $0° < θ < 90°$?
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 $0° < θ < 90°$?
Which trigonometric function is equal to $\frac{1+cos\theta-sin^2\theta}{sin\theta(1+cos\theta)}$?
Which trigonometric function is equal to $\frac{1+cos\theta-sin^2\theta}{sin\theta(1+cos\theta)}$?
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 $0° < θ < 90°$?
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 $0° < θ < 90°$?
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 $0° < θ < 90°$?
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 $0° < θ < 90°$?
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 $0° < θ < 90°$?
What is the value of 2cotθ - 3cosθ?
What is the value of 2cotθ - 3cosθ?
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?
What is the value of 3cot47° - sec43° - 2(tan23° - cosec67°)?
What is the value of 3cot47° - sec43° - 2(tan23° - cosec67°)?
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)?
What is the equation given in the problem?
What is the equation given in the problem?
What is the quadrant in which θ lies?
What is the quadrant in which θ lies?
What is the value of 2(cotθ - 3cosθ) / (3cotθ - secθ)?
What is the value of 2(cotθ - 3cosθ) / (3cotθ - secθ)?
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?
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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.
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