91Ó°ÊÓ

In Exercises 75-82, use the sum-to-product formulas to write the sum or difference as a product. $$ \cos (\phi+2 \pi)+\cos \phi $$

In Exercises 81-84, verify the identity. $$ \cos (n \pi+\theta)=(-1)^{n} \cos \theta, \quad n \text { is an integer } $$

In Exercises 77-82, use the trigonometric substitution to write the algebraic expression as a trigonometric function of \(\theta\), where \(0<\theta<\pi / 2\). $$ \sqrt{x^{2}+25}, \quad x=5 \tan \theta $$

In Exercises 77-82, use the trigonometric substitution to write the algebraic expression as a trigonometric function of \(\theta\), where \(0<\theta<\pi / 2\). $$ \sqrt{x^{2}+100}, \quad x=10 \tan \theta $$

In Exercises 75-82, use the sum-to-product formulas to write the sum or difference as a product. $$ \sin \left(x+\frac{\pi}{2}\right)+\sin \left(x-\frac{\pi}{2}\right) $$

In Exercises 81-84, verify the identity. $$ \sin (n \pi+\theta)=(-1)^{n} \sin \theta, \quad n \text { is an integer } $$

In Exercises 83-86, use the trigonometric substitution to write the algebraic equation as a trigonometric function of \(\theta\), where \(-\pi / 2<\theta<\pi / 2\). Then find \(\sin \theta\) and \(\cos \theta\). $$ 3=\sqrt{9-x^{2}}, \quad x=3 \sin \theta $$

In Exercises 81-84, verify the identity. \(a \sin B \theta+b \cos B \theta=\sqrt{a^{2}}+b^{2} \sin (B \theta+C)\), where \(C=\arctan (b / a)\) and \(a>0\)

In Exercises 83-86, use the sum-to-product formulas to find the exact value of the expression. $$ \sin 60^{\circ}+\sin 30^{\circ} $$

In Exercises 83-86, use the sum-to-product formulas to find the exact value of the expression. $$ \cos 120^{\circ}+\cos 30^{\circ} $$