Advertisements
Advertisements
प्रश्न
Prove the following identities:
`1/(cosA + sinA) + 1/(cosA - sinA) = (2cosA)/(2cos^2A - 1)`
उत्तर
`1/(cosA + sinA) + 1/(cosA - sinA)`
= `(cosA + sinA + cosA - sinA)/((cosA + sinA)(cosA - sinA)`
= `(2cosA)/(cos^2A - sin^2A)`
= `(2cosA)/(cos^2A - (1 - cos^2A))`
= `(2cosA)/(cos^2A - 1 + cos^2A)`
= `(2cosA)/(2cos^2A - 1)`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`1/(sec A - 1) + 1/(sec A + 1) = 2 cosec A cot A`
Write the value of ` sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta).`
Prove the following identity :
`sec^2A + cosec^2A = sec^2Acosec^2A`
Prove the following identity :
`sqrt(cosec^2q - 1) = "cosq cosecq"`
Prove that :(sinθ+cosecθ)2+(cosθ+ secθ)2 = 7 + tan2 θ+cot2 θ.
Prove that sin2 θ + cos4 θ = cos2 θ + sin4 θ.
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
`(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` = ?
Prove the following:
`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A
Prove the following identity:
(sin2θ – 1)(tan2θ + 1) + 1 = 0
