Question

1. Prove the following identity:
—> sin^2 theta (1+ 1/tan^2 theta) =1

Answer 1

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Step-by-step explanation:

`\sin^2(\theta)*\left(1+(1)/(\tan^2(\theta))\right)=\\\\\sin^2(\theta)*\left(1+(\cos^2(\theta))/(\sin^2(\theta))\right)=\\\\(\sin^2(\theta)\cdot(\cos^2(\theta)+\sin^2(\theta)))/(\sin^2(\theta))=\\\\\cos^2(\theta)+\sin^2(\theta)=1\qquad\text{Q.E.D.}`