Advertisements
Advertisements
Question
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Advertisements
Solution
`sqrt((1 - cosA)/(1 + cosA))`
= `sqrt((1 - cosA)/(1 + cosA) xx (1 + cosA)/(1 + cosA))`
= `sqrt((1 - cos^2A)/(1 + cosA)^2)`
= `sqrt(sin^2A/(1 + cosA)^2)`
= `sinA/(1 + cosA)`
APPEARS IN
RELATED QUESTIONS
Prove that `sqrt(sec^2 theta + cosec^2 theta) = tan theta + cot theta`
Prove the following trigonometric identities:
(1 + tan2 θ) (1 − sin θ) (1 + sin θ) = 1
Prove the following trigonometric identities.
`(1/(sec^2 theta - cos theta) + 1/(cosec^2 theta - sin^2 theta)) sin^2 theta cos^2 theta = (1 - sin^2 theta cos^2 theta)/(2 + sin^2 theta + cos^2 theta)`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`
Prove the following identity :
cosecθ(1 + cosθ)(cosecθ - cotθ) = 1
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)) + sqrt((1 - sin theta)/(1 + sin theta))` = 2 sec θ
The value of sin2θ + `1/(1 + tan^2 theta)` is equal to
Prove that `cot^2 "A" [(sec "A" - 1)/(1 + sin "A")] + sec^2 "A" [(sin"A" - 1)/(1 + sec"A")]` = 0
Prove that `(cot A)/(1 - cot A) + (tan A)/(1 - tan A) = -1`.
Prove that `(1 + sec A)/(sec A) = (sin^2A)/(1 - cos A)`.
