Podcast Beta
Questions and Answers
What is the value of cosec A - sec A?
If a cos θ + b sin θ = m and a sin θ − b cos θ = n, what is the value of a^2 + b^2?
What is the value of tan A + cot A?
What is the value of cos A + cos^2 A, if cos A + cos^2 A = 1?
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If cosec θ = 2x and cot θ = 1/2, what is the value of x?
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What is the value of sin^2 θ + cos^2 θ, if sin θ + cos θ = 1?
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What is the value of (1 + cot A + tan A)(sin A - cos A)?
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If sec A + tan A - 1 = 2 tan A, what is the value of sec A - tan A + 1?
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What is the value of (sin θ + cos θ)(tan θ + cot θ)?
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If cosec θ + cot θ = m and cosec θ - cot θ = n, what is the value of mn?
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What is the value of 1 + cos θ + sin θ, if 1 + cos θ + sin θ = 1?
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What is the value of tan θ + cot θ, if tan θ + cot θ = 2?
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If 1 + cot A - cosec A = 2, what is the value of 1 + tan A + sec A?
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What is the value of sec θ cosec θ - 2sin θ cos θ?
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What is the value of tan² θ + cot² θ?
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What is the value of tan θ + 1/cos θ, if tan θ + 1/cos θ = 2?
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Study Notes
Trigonometric Identities
- Prove that
a + b = m + nifa cos θ + b sin θ = manda sin θ - b cos θ = n.
Trigonometric Identities
- Prove that
sin 2A + sin 4A = 1ifcos A + cos² A = 1.
Trigonometric Identities
- Prove that
tan θ + (1 + sin² θ) / (cos θ) = 2 / (1 - sin θ).
Trigonometric Identities
-
(sin θ + cos θ) (tan θ + cot θ) = sec θ + cosec θ.
Trigonometric Identities
-
(sec A + tan A - 1) (sec A - tan A + 1) = 2 tan A.
Trigonometric Identities
-
(1 + cot A - cosec A) (1 + tan A + sec A) = 2.
Trigonometric Identities
-
1 / (sec A + tan A) - 1 / (sec A - tan A) = cos A cosec A - sin A sec A.
Trigonometric Identities
-
tan A - 1 / (tan A) = 2 cosec A.
Trigonometric Identities
-
tan A + 1 / (tan A) = sin A cos A.
Trigonometric Identities
-
1 + tan² A = 1 + cot² A.
Trigonometric Identities
- If
cosec θ = 2xandcot θ = 1 / x, thenx = 1 / √2.
Trigonometric Identities
-
(1 + cot A + tan A) (sin A - cos A) = sin A tan A - cot A cos A.
Trigonometric Identities
- If
cosec θ + cot θ = mandcosec θ - cot θ = n, thenmn = 1.
Trigonometric Identities
-
tan θ + cot θ = 2impliestan² θ + cot² θ = 2.
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Description
Test your knowledge of trigonometric identities with these 5 problems. Prove various identities involving sine, cosine, and tangent functions.
