Advertisements
Advertisements
प्रश्न
prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`
Advertisements
उत्तर
LHS = `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A))`
= `1/(1 + sinA) + 1/(1 - sinA)`
= `(1 - sinA + 1 + sinA)/((1 + sinA)(1 - sinA))`
= `2/(1 - sin^2A)`
= `2/cos^2A`
= `2sec^2A = 2cosec^2(90^circ - A)`
APPEARS IN
संबंधित प्रश्न
Prove that `sqrt(sec^2 theta + cosec^2 theta) = tan theta + cot theta`
Prove the following trigonometric identities.
`tan theta + 1/tan theta` = sec θ.cosec θ
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
`cosec theta (1+costheta)(cosectheta - cot theta )=1`
`(sec theta -1 )/( sec theta +1) = ( sin ^2 theta)/( (1+ cos theta )^2)`
`{1/((sec^2 theta- cos^2 theta))+ 1/((cosec^2 theta - sin^2 theta))} ( sin^2 theta cos^2 theta) = (1- sin^2 theta cos ^2 theta)/(2+ sin^2 theta cos^2 theta)`
Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`
Prove the following identity :
sinθcotθ + sinθcosecθ = 1 + cosθ
Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.
Prove that `(sin θ + "cosec" θ)/(sin θ) = 2 + cot^2θ`.
