Advertisements
Advertisements
Question
Prove that `cot^2 "A" [(sec "A" - 1)/(1 + sin "A")] + sec^2 "A" [(sin"A" - 1)/(1 + sec"A")]` = 0
Advertisements
Solution
L.H.S = `cot^2"A"[(sec"A" - 1)/(1 + sin "A")] + sec^2"A"[(sin"A" - 1)/(1 + sec"A")]`
= `(cot^2"A"(sec"A" - 1)(sec"A" + 1) + sec^2"A"(sin"A" - 1)(sin"A" + 1))/((1 + sin"A")(1 + sec"A"))`
= `(cot^2"A"(sec^2"A" - 1) + sec^2"A"(sin^2"A" - 1))/((1 + sin"A")(1 + sec"A"))`
= `(cot^2"A" xx tan^2"A" + sec^2"A"( - cos^2"A"))/((1 + sin"A")(1 + sec"A"))`
= `(cot^2"A" xx 1/cot^2"A" - sec^2"A" xx 1/sec^2"A")/((1 + sin"A")(1 + sec"A"))`
= `(1 - 1)/((1 + sin"A")(1+ sec"A"))`
= `0/((1 + sin"A")(1 + sec"A"))`
= 0
L.H.S = R.H.S
Hence it is proved.
APPEARS IN
RELATED QUESTIONS
Prove that `(tan^2 theta)/(sec theta - 1)^2 = (1 + cos theta)/(1 - cos theta)`
Prove the following trigonometric identities.
if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`
Prove the following identities:
`1/(tan A + cot A) = cos A sin A`
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
`costheta/((1-tan theta))+sin^2theta/((cos theta-sintheta))=(cos theta+ sin theta)`
Prove the following identity :
`(cot^2θ(secθ - 1))/((1 + sinθ)) = sec^2θ((1-sinθ)/(1 + secθ))`
Evaluate:
`(tan 65°)/(cot 25°)`
Prove that `sin^2 θ/ cos^2 θ + cos^2 θ/sin^2 θ = 1/(sin^2 θ. cos^2 θ) - 2`.
If 2 cos θ + sin θ = `1(θ ≠ π/2)`, then 7 cos θ + 6 sin θ is equal to ______.
(1 – cos2 A) is equal to ______.
