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If (1+sqrt(1+a))tan alpha= 1 +sqrt(1-a), then sin 4 alpha=....... |
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Answer» `(a)/(2)` `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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