How do you express ${sin}^{4} θ - {cos}^{2} θ - {tan}^{2} θ$ $sin^4theta-cos^2theta-tan^2theta$ in terms of non-exponential trigonometric functions?

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How do you express ${sin}^{4} θ - {cos}^{2} θ - {tan}^{2} θ$ $sin^4theta-cos^2theta-tan^2theta$ in terms of non-exponential trigonometric functions?

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Answer 1 · 2015-12-18T04:05:17

$f (x) = {sin}^{4} x - {cos}^{2} x - {tan}^{2} x =$ $f(x) = sin^4 x - cos^2 x - tan^2 x =$
$= ({sin}^{2} x - cos x) ({sin}^{2} x + cos x) - \frac{{sin}^{2} x}{{cos}^{2} x}$ $= (sin^2 x - cos x)(sin ^2 x + cos x) - sin^2 x/(cos^2 x)$
Replace
${sin}^{2} x$ $sin^2 x$ by $(\frac{1}{2}) (1 - cos 2 x)$ $(1/2)(1 - cos 2x)$
${cos}^{2} x$ $cos^2 x$ by $(\frac{1}{2}) (1 + cos 2 x)$ $(1/2)(1 + cos 2x)$
$f (x) = [\frac{1 - cos 2 x}{2} - cos x)] [\frac{1 - cos 2 x}{2} + cos x] - \frac{1 - cos 2 x}{1 + cos 2 x}$ $f(x) = [(1 - cos 2x)/2 - cos x)][(1 - cos 2x)/2 + cos x] - (1 - cos 2x)/(1 + cos 2x)$

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How do you express ${sin}^{4} θ - {cos}^{2} θ - {tan}^{2} θ$ $sin^4theta-cos^2theta-tan^2theta$ in terms of non-exponential trigonometric functions?

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How do you express ${sin}^{4} θ - {cos}^{2} θ - {tan}^{2} θ$ $sin^4theta-cos^2theta-tan^2theta$ in terms of non-exponential trigonometric functions?