Advertisements
Advertisements
Question
Prove the following identity :
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Advertisements
Solution
LHS = `(1 + cosA)/(1 - cosA)`
= `(1 + 1/secA)/(1 - 1/secA) = (secA + 1)/(secA - 1)`
= `(secA + 1)/(secA - 1) . (secA - 1)/(secA - 1)`
= `(sec^2A - 1)/(secA - 1)^2 = tan^2A/(secA - 1)^2` (`Q sec^2A - 1 = tan^2A`)
APPEARS IN
RELATED QUESTIONS
Prove the following identities:
`(1 + sinA)/cosA + cosA/(1 + sinA) = 2secA`
If 4 cos2 A – 3 = 0, show that: cos 3 A = 4 cos3 A – 3 cos A
`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`
If 5x = sec ` theta and 5/x = tan theta , " find the value of 5 "( x^2 - 1/( x^2))`
Prove the following Identities :
`(cosecA)/(cotA+tanA)=cosA`
Prove the following identity :
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
If A + B = 90°, show that `(sin B + cos A)/sin A = 2tan B + tan A.`
`(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` = ?
Prove that sec2θ – cos2θ = tan2θ + sin2θ
Simplify (1 + tan2θ)(1 – sinθ)(1 + sinθ)
