91Ó°ÊÓ

Establish each identity.

${\left(2a\sin \mathrm{θ}\cos \mathrm{θ}\right)}^2+a^2{\left({\cos }^2\mathrm{θ}-{\sin }^2\mathrm{θ}\right)}^2=a^2$

In Problems 81–92, use a graphing utility to solve each equation. Express the solution(s) rounded to two decimal places.

$x^2=x+3\cos \left(2x\right)$

In Problem, use a calculator to find the value of each expression rounded to two decimal places.

$\mathrm{co}{t}^{-1}\left(-\sqrt{5}\right)$

solve each equation on the interval $0≤\mathrm{θ}<2\mathrm{π}$

$\sin \mathrm{θ}-\sqrt{3}\cos \mathrm{θ}=1$

Establish each identity.

$\frac{\tan \mathrm{Î\pm }+\tan \mathrm{β}}{cot\mathrm{Î\pm }+cot\mathrm{β}}=\tan \mathrm{Î\pm }\tan \mathrm{β}$

In Problems 81–92, use a graphing utility to solve each equation. Express the solution(s) rounded to two decimal places.

$6\sin x-e^x=2,x>0$

In Problems 91-93, find the real zeros of each trigonometric function on the interval $0≤\mathrm{θ}<2\mathrm{π}$

$f\left(x\right)=\sin \left(2x\right)-\sin x$

In Problems 79-90, find the exact value of each expression.

$f\left(x\right)=\cos \left(2x\right)+\cos x$

Establish each identity.

$(\tan \mathrm{Î\pm }+\tan \mathrm{β})(1-cot\mathrm{Î\pm }cot\mathrm{β})+(cot\mathrm{Î\pm }+cot\mathrm{β})(1-\tan \mathrm{Î\pm }\tan \mathrm{β})=0$

solve each equation on the interval

$\sqrt{3}\sin \mathrm{θ}+\cos \mathrm{θ}=1$