How do you express $sin^4theta+cot^2theta$ in terms of non-exponential trigonometric functions?

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Answer 1 · 2018-06-20T16:10:44

$(1-2cos^2(x)+3cos^4(x)-cos^6(x))/(1-cos^2(x))$

Writing
$(1-cos^2(x))^2+cos^2(x)/(1-cos^2(x))$
and this is

$((1-cos^2(x))^3+cos^2(x))/(1-cos^2(x))$
Using that

$(a-b)^3=a^2-3a^2b+3ab^2-b^3$

$(1-2cos^2(x)+3cos^4(x)-cos(x)^6)/(1-cos^2(x))$

How do you express sin^4theta+cot^2theta sin^4theta+cot^2theta in terms of non-exponential trigonometric functions?