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प्रश्न
Prove that sin2 θ + cos4 θ = cos2 θ + sin4 θ.
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उत्तर
L.H.S. = sin2 θ + cos4 θ
= 1 - cos2 θ + cos4 θ
= 1 - cos2 θ (1 - cos2 θ)
= 1 - (1 - sin2 θ) sin2 θ
= 1 - sin2 θ + sin4 θ
= cos2 θ + sin4 θ
= R.H.S.
Hence proved.
संबंधित प्रश्न
Prove that:
sec2θ + cosec2θ = sec2θ x cosec2θ
Prove the following trigonometric identities:
(1 – cos2 A) cosec2 A = 1
Prove the following trigonometric identities:
tan2 A + cot2 A = sec2 A cosec2 A − 2
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
Prove the following identities:
`cotA/(1 - tanA) + tanA/(1 - cotA) = 1 + tanA + cotA`
Prove that:
(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A
Define an identity.
Prove the following identity :
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
If `sec θ = 41/40`, then find values of sin θ, cot θ, cosec θ.
`1/sin^2θ - 1/cos^2θ - 1/tan^2θ - 1/cot^2θ - 1/sec^2θ - 1/("cosec"^2θ) = -3`, then find the value of θ.
