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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