Advertisements
Advertisements
प्रश्न
Prove the following identity :
`cos^4A - sin^4A = 2cos^2A - 1`
Advertisements
उत्तर
LHS = `cos^4A - sin^4A`
= `(cos^2A - sin^2A)(cos^2A + sin^2A)`
= `{cos^2A - (1 - cos^2A)} = 2cos^2A - 1` = RHS
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x2 + y2 = m2 + n2
If `(x/a sin theta - y/b cos theta) = 1` and `(x/a cos theta + y/b sin theta) = 1`, prove that `(x^2/a^2 + y^2/b^2) = 2`.
If x = a cos θ and y = b sin θ, then b2x2 + a2y2 =
If `asin^2θ + bcos^2θ = c and p sin^2θ + qcos^2θ = r` , prove that (b - c)(r - p) = (c - a)(q - r)
If 1 + sin2α = 3 sinα cosα, then values of cot α are ______.
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
If cosA + cos2A = 1, then sin2A + sin4A = 1.
Factorize: sin3θ + cos3θ
Hence, prove the following identity:
`(sin^3θ + cos^3θ)/(sin θ + cos θ) + sin θ cos θ = 1`
