Question

Can anyone solve this .

tnxxx

Answer 1

`\cot\theta-\cot2\theta=(1)/(\sin2\theta)\\\\L_s=(\cos\theta)/(\sin\theta)-(\cos2\theta)/(\sin2\theta)=(\cos\theta)/(\sin\theta)-(\cos^2\theta-\sin^2\theta)/(2\sin\theta\cos\theta)\\\\=(\cos\theta\cdot2\cos\theta)/(\sin\theta\cdot2\cos\theta)-(cos^2\theta-\sin^2\theta)/(2\sin\theta\cos\theta)=(2\cos^2\theta)/(2\sin\theta\cos\theta)-(\cos^2\theta-\sin^2\theta)/(2\sin\theta\cos\theta)`

`=(2\cos^2\theta-\cos^2\theta+\sin^2\theta)/(\sin2\theta)=(\cos^2+\sin^2\theta)/(\sin2\theta)=(1)/(\sin2\theta)=R_s\\\\\text{Used:}\\\\\cot x=(\cos x)/(\sin x)\\\\\sin2x=2\sin x\cos x\\\\\sin^2x+\cos^2x=1`