Question

prove that 1 + cos² 2x = 2 (cos^4+ x + sin^4x
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Answer 1

LHS:

2[cos⁴(x) + sin⁴(x)]

=2{[cos²(x) + sin2(x)]² − 2sin²(x).cos²(x)}

=2[1 − 2sin²(x).cos²(x)]

=2 − 4sin²(x)cos²(x)

=2 − 4.[1−cos(2x)].[1+cos(2x)]

2 2

=2 − [1 − cos²(2x)]

=2 + cos²(2x) − 1

=1+cos²(2x)

HENCE PROVED!!!