How do you verify the identity below?

Question

$4cos^2(x)-sin^2(x)=5cos^2(x)-1$

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Answer 1 · 2018-03-06T15:51:24

See Below

Use the identity
$sin^2x+cos^2x=1$

$sin^2x=1-cos^2x$

LHS: $4cos^2x-sin^2x$

$=4cos^2x-(1-cos^2x)$

$=4cos^2x-1+cos^2x$

$=4cos^2x+cos^x-1$

$=5 cos^2x -1$

=RHS