Advertisements
Advertisements
Question
Prove the following identities:
sec2 A . cosec2 A = tan2 A + cot2 A + 2
Advertisements
Solution
L.H.S. = sec2 A . cosec2 A
= `1/(cos^2A) * 1/(sin^2A)`
= `1/(cos^2A sin^2A)`
= `(sin^2A + cos^2A)/(cos^2A sin^2A)`
= `1/(cos^2A) + 1/(sin^2A)`
= sec2 A + cosec2 A
= 1 + tan2 A + 1 + cot2 A ...(∵ sec2 A = 1 + tan2 A and cosec2 A = 1 + cot2 A)
= tan2 A + cot2 A + 2 = R.H.S.
APPEARS IN
RELATED QUESTIONS
If cosθ + sinθ = √2 cosθ, show that cosθ – sinθ = √2 sinθ.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
`(sintheta - 2sin^3theta)/(2costheta - costheta) =tan theta`
Prove the following trigonometric identities.
`tan theta - cot theta = (2 sin^2 theta - 1)/(sin theta cos theta)`
Prove the following trigonometric identities.
(1 + cot A − cosec A) (1 + tan A + sec A) = 2
Prove the following trigonometric identities.
`(cot A + tan B)/(cot B + tan A) = cot A tan B`
`1 + (tan^2 θ)/((1 + sec θ)) = sec θ`
For ΔABC , prove that :
`tan ((B + C)/2) = cot "A/2`
Prove that `sin^2 θ/ cos^2 θ + cos^2 θ/sin^2 θ = 1/(sin^2 θ. cos^2 θ) - 2`.
Which is not correct formula?
Prove that `(1 + sec theta - tan theta)/(1 + sec theta + tan theta) = (1 - sin theta)/cos theta`
