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Magazine Problem 71
Use identities to write each expression as a single function of \(x\) or \(\theta\). $$\cos \left(60^{\circ}+\theta\right)$$
Problem 71
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. $$\frac{1-\cos ^{2}(-\theta)}{1+\tan ^{2}(-\theta)}$$
Problem 72
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. $$\frac{1-\sin ^{2}(-\theta)}{1+\cot ^{2}(-\theta)}$$
Problem 72
Use identities to write each expression as a single function of \(x\) or \(\theta\). $$\cos \left(\theta-30^{\circ}\right)$$
Problem 72
Verify that each trigonometric equation is an identity. $$\left(1-\cos ^{2} \alpha\right)\left(1+\cos ^{2} \alpha\right)=2 \sin ^{2} \alpha-\sin ^{4} \alpha$$
Problem 73
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. $$\sec \theta-\cos \theta$$
Problem 73
Verify that each trigonometric equation is an identity. $$\frac{1-\cos x}{1+\cos x}=\csc ^{2} x-2 \csc x \cot x+\cot ^{2} x$$
Problem 73
Use an identity to write each expression as a single trigonometric function. $$\frac{1-\cos 59.74^{\circ}}{\sin 59.74^{\circ}}$$
Problem 73
Use identities to write each expression as a single function of \(x\) or \(\theta\). $$\cos \left(\frac{3 \pi}{4}-x\right)$$
Problem 74
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. $$\csc \theta-\sin \theta$$
