What is the value of [[(sinx - 2sin³x)/(2cos³x - cosx)]² + 1, x ≠ 45°]?
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Correct answer: B
Explanation
Has been given :
[(sinx − 2sin³x) / (2cos³x − cosx)]² + 1 , x ≠ 45°
According to the formula:
sinx − 2sin³x = sinx(1 − 2sin²x)
2cos³x − cosx = cosx(2cos²x − 1)
2cos²x − 1 = 1 − 2sin²x
(sinx − 2sin³x) / (2cos³x − cosx)
= sinx(1 − 2sin²x) / [cosx(1 − 2sin²x)]
= sinx / cosx
=tanx
(tanx)² + 1
= tan²x + 1
= sec²x