91Ó°ÊÓ

Using Inverse Functions In Exercises \(63-74,\) use inverse functions where needed to find all solutions of the equation in the interval \(0,2 \pi )\) $$\sec ^{2} x-4 \sec x=0$$

Solving a Trigonometric Equation In Exercises \(69-74\) , find all solutions of the equation in the interval \(\cos \left(x+\frac{\pi}{4}\right)-\cos \left(x-\frac{\pi}{4}\right)=1\)

Using Inverse Functions In Exercises \(63-74,\) use inverse functions where needed to find all solutions of the equation in the interval \(0,2 \pi )\) $$\sec ^{2} x+2 \sec x-8=0$$

Determine whether the equation is an identity, and give a reason for your answer. \(\sin \theta \csc \theta=1\)

Verifying a Trigonometric ldentity, verify the identity. $$ \cos \left(\frac{\pi}{3}+x\right)+\cos \left(\frac{\pi}{3}-x\right)=\cos x $$

Think About It. Explain why the equation is not an identity and find one value of the variable for which the equation is not true. $$\tan \theta=\sqrt{\sec ^{2} \theta-1}$$

Solving a Trigonometric Equation In Exercises \(69-74\) , find all solutions of the equation in the interval \(\sin \left(x+\frac{\pi}{6}\right)-\sin \left(x-\frac{7 \pi}{6}\right)=\frac{\sqrt{3}}{2}\)

Solving a Trigonometric Equation In Exercises \(69-74\) , find all solutions of the equation in the interval \(\tan (x+\pi)+2 \sin (x+\pi)=0\)

Using Inverse Functions In Exercises \(63-74,\) use inverse functions where needed to find all solutions of the equation in the interval \(0,2 \pi )\) $$\csc ^{2} x+3 \csc x-4=0$$

Think About It. Explain why the equation is not an identity and find one value of the variable for which the equation is not true. $$1-\cos \theta=\sin \theta$$