Advertisements
Advertisements
Question
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
Advertisements
Solution
cosec4 A (1 – cos4 A) – 2 cot2 A
= cosec4 A (1 – cos2 A) (1 + cos2 A) – 2 cot2 A
= cosec4 A (sin2 A) (1 + cos2 A) – 2 cot2 A
= cosec2 A (1 + cos2 A) – 2 cot2 A
= `cosec^2A + cos^2A/sin^2A - 2cot^2A `
= cosec2 A + cot2 A – 2 cot2 A
= cosec2 A – cot2 A
= 1
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
(sec2 θ − 1) (cosec2 θ − 1) = 1
Prove the following trigonometric identities.
`(tan A + tan B)/(cot A + cot B) = tan A tan B`
Prove the following identities:
`(1 + sinA)/cosA + cosA/(1 + sinA) = 2secA`
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
Prove the following identities:
`(cos theta "cosec" theta - sin theta sec theta )/(cos theta + sin theta) = "cosec" theta - sec theta`
If cos A + cos2 A = 1, then sin2 A + sin4 A =
Prove that:
(cosec θ - sinθ )(secθ - cosθ ) ( tanθ +cot θ) =1
Prove the following identity:
`cosA/(1 + sinA) = secA - tanA`
If tan θ = 3, then `(4 sin theta - cos theta)/(4 sin theta + cos theta)` is equal to ______.
If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.
