Question
Verify that each equation is an identity. See Examples $1-5$$$\sin ^{4} \theta-\cos ^{4} \theta=2 \sin ^{2} \theta-1$$
Step 1
Step 1: We start with the left hand side of the equation: $$\sin ^{4} \theta-\cos ^{4} \theta$$ This can be written as: $$(\sin ^{2} \theta)^{2}-(\cos ^{2} \theta)^{2}$$ which is of the form $a^{2}-b^{2}$. Show more…
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