Advertisements
Advertisements
Question
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`
Advertisements
Solution
`sqrt((1 + sinA)/(1 - sinA))`
= `sqrt((1 + sinA)/(1 - sinA) xx (1 - sinA)/(1 - sinA))`
= `sqrt((1 - sin^2A)/(1 - sinA)^2)`
= `sqrt(cos^2A/((1 - sinA)^2)`
= `cosA/(1 - sinA)`
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`[tan θ + 1/cos θ]^2 + [tan θ - 1/cos θ]^2 = 2((1 + sin^2 θ)/(1 - sin^2 θ))`
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
Prove the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
Prove the following identities:
`1/(cosA + sinA) + 1/(cosA - sinA) = (2cosA)/(2cos^2A - 1)`
If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`
If x = a sin θ and y = b cos θ, what is the value of b2x2 + a2y2?
If x = a sec θ and y = b tan θ, then b2x2 − a2y2 =
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
If cosθ = `5/13`, then find sinθ.
Prove that `(sin 70°)/(cos 20°) + (cosec 20°)/(sec 70°) - 2 cos 70° xx cosec 20°` = 0.
