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If `2 tan^-1 (cosx)=tan^-1 (2 cosecx)` then `sinx + cosx=`A. `2sqrt2`B. `sqrt2`C. `(1)/(sqrt2)`D. `(1)/(2)` |
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Answer» Correct Answer - B Given `2tan^(-1)(cos x)=tan^(-1)(2cosec x)` `Rightarrow tan^(-1) (2cos x)/(1-cos^(2)x)=tan^(1)((2)/(sin x))` `Rightarrow (2cos x)/(1-cos^2x)=(2)/(sin x) Rightarrow (cos x)/(sin^(2)x)=(1)/(sin x)` `Rightarrow (cos x)/(sin x)=1 [therefore sin x ne 0]` `Rightarrow tan x=1 Rightarrow x= (pi)/(4)` Now, `sin x+cos x=sin"" (pi)/(4)+cos ""(pi)/(4)` `=(1)/(sqrt2)+(1)/(sqrt2)=sqrt2` |
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