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प्रश्न
Evaluate the following:
`tan{2tan^-1 1/5-pi/4}`
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उत्तर
`tan{2tan^-1 1/5-pi/4}`
`= tan [tan^-1 (2xx1/5)/(1-(1/5)^2) - tan^-1 1]`
`= tan [tan^-1 (2/5)/(24/25) - tan^-1 1]`
`= tan[tan^-1 10/24 - tan^-1]`
`= tan [(tan^-1 10/24 - 1)/(1+ 10/24 xx1)]`
`= tan [tan^-1 (10-24/24)/(24+10/24)]`
`=tan [tan^-1 -14/34]`
`= tan [tan^-1 -7/17]`
`= -7/17`
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