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Mathematics

Prove the following identities :

(cos A + sin A)2 + (cos A - sin A)2 = 2

Trigonometric Identities

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Answer

Solving L.H.S. of the equation :

⇒ (cos A + sin A)2 + (cos A - sin A)2

⇒ cos2 A + sin2 A + 2 cos A sin A + cos2 A + sin2 A - 2 cos A sin A

⇒ 2(sin2 A + cos2 A) + 2cos A sin A - 2cos A sin A

As, sin2 A + cos2 A = 1

⇒ 2 × 1

⇒ 2.

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

Hence, proved that (cos A + sin A)2 + (cos A - sin A)2 = 2.

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