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Mathematics

Prove the following:

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

Trigonometrical Ratios

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Answer

Solving L.H.S. of equation : (sin A + cos A)2 + (sin A - cos A)2 = 2, we get,

⇒ (sin A + cos A)2 + (sin A - cos A)2

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

Since, sin2 A + cos2 A = 1.

⇒ 1 + 2 sin A cos A + 1 - 2 sin A cos A

⇒ 2.

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

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

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