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If tan^(-1)(1/(1+1. 2))+tan^(-1)(1/(1+2....

If `tan^(-1)(1/(1+1. 2))+tan^(-1)(1/(1+2. 3))++tan^(-1)(1/(1+n.(n+1)))=tan^(-1)theta,` then find the value of `thetadot`

Text Solution

Verified by Experts

The correct Answer is:
`2sqrt(2)`
`cot(11(1^(@))/(4))+tan(112(1^(@))/(2))-cot(112(1^(@))/(2))-tan(11(1^(@))/(4))`
`=(cot11(1^(@))/(4)-tan11(1^(@))/(4))+tan(90^(@)+22(1^(@))/(2))-cot(90^(@)+22(1^(@))/(2))`
`=(2(1-tan^(2)11(1^(@))/(4)))/(2tan11(1^(@))/(4))-cot22(1^(@))/(2)+tan22(1^(@))/(2)`
`=2cot22(1^(@))/(2)-cot22(1^(@))/(2)+tan22(1^(@))/(2)`
`cot 22(1^(@))/(2)+tan22(1^(@))/(2)`
`=(sqrt(2)+1)+(sqrt(2)-1)`
`=2sqrt(2)`.
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