Advertisements
Advertisements
प्रश्न
Prove the following identities:
(cosec A + sin A) (cosec A – sin A) = cot2 A + cos2 A
उत्तर
L.H.S. = (cosec A + sin A) (cosec A – sin A)
= (cosec2 A – sin2 A) ...[∵ (a + b) (a – b) = a2 – b2]
= 1 + cot2 A – sin2 A
= cot2 A + 1 – sin2 A
= cot2 A + cos2 A ...(∵ 1 – sin2 A = cos2 A)
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1
Prove the following trigonometric identities.
`cot theta - tan theta = (2 cos^2 theta - 1)/(sin theta cos theta)`
Prove the following trigonometric identities.
`sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A + 1) = 1`
Prove the following identities:
`1/(cosA + sinA) + 1/(cosA - sinA) = (2cosA)/(2cos^2A - 1)`
`tan theta/(1+ tan^2 theta)^2 + cottheta/(1+ cot^2 theta)^2 = sin theta cos theta`
What is the value of (1 − cos2 θ) cosec2 θ?
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`
Choose the correct alternative:
Which is not correct formula?
If 5 sec θ – 12 cosec θ = 0, then find values of sin θ, sec θ
