Write $cos^4x-tan^2x$ in terms of (a) $cos^2x$ and (b) $sin^2x$ ?

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Answer 1 · 2018-02-14T14:23:03

Please see below.

In terms of $cos^2x$

$cos^4x-tan^2x$

= $(cos^2x)^2-sin^2x/cos^2x$

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

= $(cos^2x)^2-1/cos^2x+1$

In terms of $sin^2x$

$cos^4x-tan^2x$

= $(cos^2x)^2-sin^2x/cos^2x$

= $(1-sin^2x)^2-sin^2x/(1-sin^2x)$

Write cos^4x-tan^2xcos^4x-tan^2x in terms of (a) cos^2xcos^2x and (b) sin^2xsin^2x?