Advertisements
Advertisements
Question
Prove that:
`1/(cosA + sinA - 1) + 1/(cosA + sinA + 1) = cosecA + secA`
Advertisements
Solution
L.H.S. = `1/(cosA + sinA - 1) + 1/(cosA + sinA + 1)`
= `(cosA + sinA + 1 + cosA + sinA - 1)/((cosA + sinA)^2 - 1)`
= `(2(cosA + sinA))/(cos^2A + sin^2A + 2cosAsinA - 1)`
= `(2(cosA + sinA))/(1 + 2cosAsinA - 1)`
= `(cosA + sinA)/(cosAsinA)`
= `cosA/(cosAsinA) + sinA/(cosAsinA)`
= `1/sinA + 1/cosA`
= cosec A + sec A = R.H.S.
APPEARS IN
RELATED QUESTIONS
`(1+tan^2A)/(1+cot^2A)` = ______.
Show that `sqrt((1-cos A)/(1 + cos A)) = sinA/(1 + cosA)`
Prove the following trigonometric identities.
`"cosec" theta sqrt(1 - cos^2 theta) = 1`
Prove the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`
The value of (1 + cot θ − cosec θ) (1 + tan θ + sec θ) is
If x = a cos θ and y = b sin θ, then b2x2 + a2y2 =
Prove the following identity :
`(1 - cos^2θ)sec^2θ = tan^2θ`
If cot θ + tan θ = x and sec θ – cos θ = y, then prove that `(x^2y)^(2/3) – (xy^2)^(2/3)` = 1
Prove that `sqrt((1 + cos A)/(1 - cos A)) = "cosec" A + cot A`.
