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If `(1+sqrt(1+a))tan alpha= 1 +sqrt(1-a)`, then `sin 4 alpha=.......`A. `(a)/(2)`B. aC. 2aD. `a^(2/3)` |
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Answer» Correct Answer - B 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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