Question
Use the sum identities to prove the double-angle identities listed in Theorem 0.26. (Hint: Note that $2 \theta$ is equal to $\theta+\theta$.)
Step 1
We can rewrite this as $\sin (\theta+\theta)$. Show more…
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Use the first Pythagorean identity $\sin ^{2} \theta+\cos ^{2} \theta=1$ to prove the second and third Pythagorean identities listed in Theorem 0.26. (Hint: To prove the second identity, divide both sides of the first identity by $\cos ^{2} x$. A similar strategy will prove the third identity.)
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Use the first Pythagorean identity $\sin ^{2} \theta+\cos ^{2} \theta=1$ to prove the second and third Pythagorean identities listed in Theorem $0.26$. (Hint: To prove the second identity, divide both sides of the first identity by $\cos ^{2} x$. A similar strategy will prove the third identity.)
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