Prove that : 2 sin 2 A + cos 4 A = 1 + sin 4 A

Solving L.H.S. of the equation : ⇒ 2 sin 2 A + cos 4 A ⇒ 2 sin 2 A + (cos 2 A) 2 By formula, cos 2 A = 1 - sin 2 A ⇒ 2 sin 2 A + (1 - sin 2 A) 2 ⇒ 2 sin 2 A + 1 + sin 4 A - 2 sin 2 A ⇒ 1 + sin 4 A. Since, L.H.S. = R.H.S. Hence, proved that 2 sin 2 A + cos 4 A = 1 + sin 4 A.

Mathematics

Prove that :
2 sin² A + cos⁴ A = 1 + sin⁴ A

Trigonometric Identities

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Answer

Solving L.H.S. of the equation :

⇒ 2 sin² A + cos⁴ A

⇒ 2 sin² A + (cos² A)²

By formula,

cos² A = 1 - sin² A

⇒ 2 sin² A + (1 - sin² A)²

⇒ 2 sin² A + 1 + sin⁴ A - 2 sin² A

⇒ 1 + sin⁴ A.

Since, L.H.S. = R.H.S.

Hence, proved that 2 sin² A + cos⁴ A = 1 + sin⁴ A.

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Mathematics

Prove that :2 sin2 A + cos4 A = 1 + sin4 A

Trigonometric Identities

Answer

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Prove that :
2 sin² A + cos⁴ A = 1 + sin⁴ A