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

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

Discussion

`tan^(-1)[(cosx)/(1+sinx)]`is equal to`pi/4-x/2,forx in (-pi/2,(3pi)/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-(3pi)/2,pi/2)`
The value of `sin^(-1)(sin12)+sin^(-1)(cos12)=`
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