1.

If (1+sqrt(1+a))tan alpha= 1 +sqrt(1-a), then sin 4 alpha=.......

Answer»

`(a)/(2)`
a
2a
`a^(2/3)`

Solution :LET `a=sin4thetaimpliessqrt(1+a)=cos2theta+sin2theta` and `sqrt(1-a)=cos2theta-sin2theta`
`because(1+sqrt(1+a))TAN ALPHA=1+sqrt(1-a)`
`implies(1+cos2theta+sin2theta)tanalpha=1+cos2theta-sin2theta`
`=2costheta(costheta+sintheta)tan alpha=2costheta(costheta-sintheta)`
`implies(costheta+sintheta)/(costheta-sintheta)=cotalphaimplies(1+tantheta)/(1-tantheta)=COTALPHA`
`impliestan((pi)/(4)+theta)=tan((pi)/(2)-alpha)=alpha=(pi)/(4)-theta`
`=sin4alpha=sin(pi-4theta)=sin4theta=a`


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