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प्रश्न
Prove that: sin4 θ + cos4θ = 1 - 2sin2θ cos2 θ.
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उत्तर
LHS = (sin2θ)2 + (cos2 θ)2 + 2 sin2θ cos2θ - 2 sin2θ cos2θ
= ( sin2θ + cos2θ )2 - 2 sin2θ cos2θ
= 1 - 2 sin2θ cos2θ
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`
Prove the following identities:
`((1 + tan^2A)cotA)/(cosec^2A) = tan A`
If `secθ = 25/7 ` then find tanθ.
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`
If sec θ = `25/7`, then find the value of tan θ.
Prove that sin (90° - θ) cos (90° - θ) = tan θ. cos2θ.
If tan A + sin A = m and tan A − sin A = n, then show that `m^2 - n^2 = 4 sqrt (mn)`.
Prove that (cosec A - sin A)( sec A - cos A) sec2 A = tan A.
Prove the following identities: cot θ - tan θ = `(2 cos^2 θ - 1)/(sin θ cos θ)`.
