Advertisements
Advertisements
Question
Prove the following identity :
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
Advertisements
Solution
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
= `(1 + cosA)/(1 - cosA).(1 + cosA)/(1 + cosA)`
= `((1 + cosA)^2)/(1 - cos^2A) = (1 + cosA)^2/sin^2A`
= `[(1 + cosA)/sinA]^2 = [1/sinA + cosA/sinA]^2`
= `(cosecA + cotA)^2`
APPEARS IN
RELATED QUESTIONS
Prove the following identities:
`(i) (sinθ + cosecθ)^2 + (cosθ + secθ)^2 = 7 + tan^2 θ + cot^2 θ`
`(ii) (sinθ + secθ)^2 + (cosθ + cosecθ)^2 = (1 + secθ cosecθ)^2`
`(iii) sec^4 θ– sec^2 θ = tan^4 θ + tan^2 θ`
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = cosec A - cot A`
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos ^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`
If `cos theta = 7/25 , "write the value of" ( tan theta + cot theta).`
Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`
If x = a sec θ and y = b tan θ, then b2x2 − a2y2 =
Prove the following identities:
`(1 - tan^2 θ)/(cot^2 θ - 1) = tan^2 θ`.
Prove that (1 – cos2A) . sec2B + tan2B (1 – sin2A) = sin2A + tan2B.
