Advertisements
Advertisements
प्रश्न
Prove the following identities:
`cot^2A/(cosecA + 1)^2 = (1 - sinA)/(1 + sinA)`
Advertisements
उत्तर
R.H.S. = `(1 - sinA)/(1 + sinA)`
= `(1 - 1/(cosecA))/(1 + 1/(cosecA))`
= `(cosecA - 1)/(cosecA + 1)`
= `(cosecA - 1)/(cosecA + 1) xx (cosecA + 1)/(cosecA + 1)`
= `(cosec^2A - 1)/(cosecA + 1)^2 = cot^2A/(cosecA + 1)^2` ...(∵ cosec2 A – 1 = cot2 A)
= L.H.S.
APPEARS IN
संबंधित प्रश्न
Prove that `sqrt(sec^2 theta + cosec^2 theta) = tan theta + cot theta`
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
Prove the following trigonometric identities.
`(cot A - cos A)/(cot A + cos A) = (cosec A - 1)/(cosec A + 1)`
Prove the following identities:
(cosec A + sin A) (cosec A – sin A) = cot2 A + cos2 A
Prove the following identities:
`cosecA + cotA = 1/(cosecA - cotA)`
Simplify : 2 sin30 + 3 tan45.
\[\frac{x^2 - 1}{2x}\] is equal to
Prove that `(sec θ - 1)/(sec θ + 1) = ((sin θ)/(1 + cos θ ))^2`
If A + B = 90°, show that `(sin B + cos A)/sin A = 2tan B + tan A.`
Prove that cot2θ – tan2θ = cosec2θ – sec2θ.
