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Prove that cot(pi/4-2cot^(- 1)3)=7...

Prove that `cot(pi/4-2cot^(- 1)3)=7`

Text Solution

Verified by Experts

Let `cot^(-1)3=theta`
the equation reduces to=>`Cot(pi/4-2theta)=1/(tan(pi/4-2theta))=(1+tan2theta)/(1-tan2theta)`
since `cottheta=3 ` then `tantheta=1/3`
`tan2theta=(2tantheta)/(1-tan^2(theta))`=> substituting value we get,
`tan2theta=3/4`
thus`(1+tan2theta)/(1-tan2theta)=7`
hence proved
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