1.5 Inverse trig-functions practice 4

Solve [math]\dfrac{1}{4}(2\cos(2x)+\sec(2x))=\dfrac{3}{4}[/math] on the interval [math]-\pi\leq x\leq0[/math]. Write your answer in accending order.

Solve [math]\cot\theta\cos\theta+4\cot\theta=-3\cot\theta[/math] on the interval [math]0\leq\theta\leq2\pi[/math]. Write your answer in accending order.

Solve [math]\cos(2\theta)+3\cos\theta+2=0[/math].

How many solutions does the equation [math]\sin2x=\tan x[/math] have where [math]x\in[-\pi,\pi][/math]?

What is the range of the function [math]y=\cos(\tan^{-1}x)[/math]

Which of the following statement(s) is/are true?

Find the exact value of [math]\sin\left(\cos^{-1}\dfrac{5}{13}-\sin^{-1}\dfrac{3}{5}\right)[/math].

Evaluate the following numbers. If your answer is undefined, write “undef”.

(a) [math]\cos^{-1}\left(\cos\dfrac{5\pi}{4}\right)[/math]

(b) [math]\tan\left(\sin^{-1}\left(-\dfrac{4}{5}\right)\right)[/math]

(c) [math]\sin^{-1}\left(\dfrac{\pi}{2}\right)[/math]

(d) [math]\cos^{-1}\left(\sin\dfrac{4\pi}{5}\right)[/math]

Find all solutions to the equation [math]2\cos^2x=1[/math].

Find the summation of the all solutions to the equation [math]4\cos x\cos3x+2\cos x-6\cos3x-3=0[/math] where [math]-\pi\leq x\leq\pi[/math].