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प्रश्न
Prove the following identity :
`cos^4A - sin^4A = 2cos^2A - 1`
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उत्तर
LHS = `cos^4A - sin^4A`
= `(cos^2A - sin^2A)(cos^2A + sin^2A)`
= `{cos^2A - (1 - cos^2A)} = 2cos^2A - 1` = RHS
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संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 + sec theta)/sec theta = (sin^2 theta)/(1 - cos theta)`
Prove the following identities:
`(1+ sin A)/(cosec A - cot A) - (1 - sin A)/(cosec A + cot A) = 2(1 + cot A)`
`sin^6 theta + cos^6 theta =1 -3 sin^2 theta cos^2 theta`
If x = a sin θ and y = bcos θ , write the value of`(b^2 x^2 + a^2 y^2)`
Define an identity.
Prove the following identities:
`(sec"A"-1)/(sec"A"+1)=(sin"A"/(1+cos"A"))^2`
Prove the following identity :
`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2Acos^2B)`
If `asin^2θ + bcos^2θ = c and p sin^2θ + qcos^2θ = r` , prove that (b - c)(r - p) = (c - a)(q - r)
Prove that ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A
Complete the following activity to prove:
cotθ + tanθ = cosecθ × secθ
Activity: L.H.S. = cotθ + tanθ
= `cosθ/sinθ + square/cosθ`
= `(square + sin^2theta)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ....... ∵ `square`
= `1/sinθ xx 1/cosθ`
= `square xx secθ`
∴ L.H.S. = R.H.S.
