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Questions
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
Prove the following:
(sin A + cos A)2 + (cos A – sin A)2 = 2
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Solution
L.H.S. = (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 + 2 cos2 A
= 2(sin2 A + cos2 A) ...(∵ sin2 A + cos2 A = 1)
= 2 × 1
= 2
= R.H.S.
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