1.

Solve for `x :``2tan^(-1)(sinx)=tan^(-1)(2secx), x!=pi/2`

Answer» `2tan^-1(sinx) = tan^-1(2secx)`
Applying `tan` both sides,
`=> tan(2tan^-1(sinx)) = tan(tan^-1(2secx))`
`=>(2tan(tan^-1(sinx)))/(1-tan^2(tan^-1(sinx))) = 2secx`
`=>(2sinx)/(1-sin^2x) = 2secx`
`=>sinx/cos^2x = 1/cosx`
`=>six/cosx = 1`
`=>tanx = 1`
`=>x = npi+pi/4`


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