Question

Verify identity:
sinˆ2(2t)/sinˆ2(t)=4-4sinˆ2(t)

Answer 1

LHS/RHS proof.
\[\huge \frac{\sin^22t}{\sin^2 t}=4-4\sin^2 t\]
\[\huge LHS=\frac{\sin^22t}{\sin^2 t}\]
\[\huge =\frac{(2\sin t\cos t)^2}{\sin^2 t}\]
\[\huge =\frac{4\sin^2 t\cos^2 t}{\sin^2 t}\]
\[\huge =4\cos^2 t\]
Use your knowledge of trig identities
\[\sin^2 t+\cos^2 t=1\]
\[\cos^2 t=1-\sin^2 t\]
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\[\huge=4(1-\sin^2 t)\]
\[\huge =4-4\sin^2 t\]
\[\huge =RHS\]

Answer 2

Thank you!