Advertisements
Advertisements
प्रश्न
Prove the following identities:
`1 - cos^2A/(1 + sinA) = sinA`
Advertisements
उत्तर
L.H.S. = `1 - cos^2A/(1 + sinA)`
= `(1 + sinA - cos^2A)/(1 + sinA)`
= `(sinA + sin^2A)/(1 + sinA)`
= `(sinA(1 + sinA))/(1 + sinA)`
= sin A = R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`sqrt((1+sinA)/(1-sinA)) = secA + tanA`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`
Prove the following trigonometric identities.
(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1
Prove the following trigonometric identities.
sin2 A cos2 B − cos2 A sin2 B = sin2 A − sin2 B
Prove that:
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
Prove that:
(tan A + cot A) (cosec A – sin A) (sec A – cos A) = 1
Evaluate:
`(tan 65°)/(cot 25°)`
Prove that `sqrt((1 + cos A)/(1 - cos A)) = (tan A + sin A)/(tan A. sin A)`
Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.
If cosec A – sin A = p and sec A – cos A = q, then prove that `(p^2q)^(2/3) + (pq^2)^(2/3) = 1`.
