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Magazine Problem 76
Write each expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression and all functions are of \(\theta\) only. $$(\sin \theta-\cos \theta)(\csc \theta+\sec \theta)$$
Problem 77
Use identities to write each expression as a single function of \(x\) or \(\theta\). $$\sin \left(\frac{\pi}{4}+x\right)$$
Problem 77
Use an identity to write each expression as a single trigonometric function. $$\pm \sqrt{\frac{1-\cos 8 \theta}{1+\cos 8 \theta}}$$
Problem 77
Write each expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression and all functions are of \(\theta\) only. $$\sin \theta(\csc \theta-\sin \theta)$$
Problem 77
Verify that each trigonometric equation is an identity. $$\sec x-\cos x+\csc x-\sin x-\sin x \tan x=\cos x \cot x$$
Problem 78
Use an identity to write each expression as a single trigonometric function. $$\pm \sqrt{\frac{1-\cos 5 A}{1+\cos 5 A}}$$
Problem 78
Verify that each trigonometric equation is an identity. $$\sin ^{3} \theta+\cos ^{3} \theta=(\cos \theta+\sin \theta)(1-\cos \theta \sin \theta)$$
Problem 78
Use identities to write each expression as a single function of \(x\) or \(\theta\). $$\sin \left(\frac{3 \pi}{4}-x\right)$$
Problem 79
Write each expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression and all functions are of \(\theta\) only. $$\frac{1+\tan ^{2} \theta}{1+\cot ^{2} \theta}$$
Problem 79
Use identities to write each expression as a single function of \(x\) or \(\theta\). $$\sin \left(270^{\circ}-\theta\right)$$
