Advertisements
Advertisements
प्रश्न
Prove that:
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
उत्तर
L.H.S. = `(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA)`
= `((cos^3A + sin^3A)(cosA - sinA) + (cos^3A - sin^3A)(cosA + sinA))/(cos^2A - sin^2A)`
= `(cos^4A - cos^3AsinA + sin^3AcosA - sin^4A + cos^4A + cos^3AsinA - sin^3AcosA - sin^4A)/(cos^2A - sin^2A)`
= `(2(cos^4A - sin^4A))/(cos^2A - sin^2A)`
= `(2(cos^2A + sin^2A)2(cos^2A - sin^2A))/(cos^2A - sin^2A)`
= 2(cos2 A + sin2 A)
= 2 = R.H.S. ...(∵ cos2 A + sin2 A = 1)
APPEARS IN
संबंधित प्रश्न
Prove that (cosec A – sin A)(sec A – cos A) sec2 A = tan A.
Prove the following trigonometric identities.
(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1
Prove the following trigonometric identities.
`(cos^2 theta)/sin theta - cosec theta + sin theta = 0`
Prove the following trigonometric identities. `(1 - cos A)/(1 + cos A) = (cot A - cosec A)^2`
If x = a sin θ and y = b cos θ, what is the value of b2x2 + a2y2?
\[\frac{1 - \sin \theta}{\cos \theta}\] is equal to
Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.
Prove the following identities: sec2 θ + cosec2 θ = sec2 θ cosec2 θ.
If cos A = `(2sqrt("m"))/("m" + 1)`, then prove that cosec A = `("m" + 1)/("m" - 1)`
Prove that `(cot A - cos A)/(cot A + cos A) = (cos^2 A)/(1 + sin A)^2`
