Advertisements
Advertisements
Question
Prove that `( tan A + sec A - 1)/(tan A - sec A + 1) = (1 + sin A)/cos A`.
Advertisements
Solution
LHS = `( tan A + sec A - 1)/(tan A - sec A + 1)`
= `(( tan A + sec A) - (sec^2 A - tan^2 A))/((tan A - sec A) + 1)`
= `(( tan A + sec A)( 1 - sec A + tan A))/(tan A - sec A + 1)`
= tan A + sec A
= `sin A/cos A + 1/cos A = (1 + sin A)/cos A`
= RHS
Hence proved.
RELATED QUESTIONS
Prove the following identities:
`(i) cos4^4 A – cos^2 A = sin^4 A – sin^2 A`
`(ii) cot^4 A – 1 = cosec^4 A – 2cosec^2 A`
`(iii) sin^6 A + cos^6 A = 1 – 3sin^2 A cos^2 A.`
Prove the following trigonometric identities.
`(cot A - cos A)/(cot A + cos A) = (cosec A - 1)/(cosec A + 1)`
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = cosec A - cot A`
If sin A + cos A = p and sec A + cosec A = q, then prove that : q(p2 – 1) = 2p.
If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that (m2 + n2) = (a2 + b2).
If `cos theta = 2/3 , " write the value of" (4+4 tan^2 theta).`
If sin θ − cos θ = 0 then the value of sin4θ + cos4θ
1 + cot2θ = ?
`sqrt((1 - cos^2theta) sec^2 theta) = tan theta`
