If cos A + cos2 A = 1, then the value of sin4 A + sin6 A is:
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Correct answer: B
Explanation
The correct answer is option 2 i.e. cos A.
Given that, cos A + cos2 A = 1
⇒ cos A = 1 - cos2 A
⇒ cos A = sin2 A ....(i)
According to the given question,
sin4 A + sin6 A
⇒ sin2 A(sin2 A + sin4 A)
⇒ sin2 A(sin2 A + cos2 A) (from equation (i))
⇒ sin2 A × 1
⇒ cos A
Hence the required answer is cos A.