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1.Solve for X: 2 tan-" (cos x) = tan- (2 cosec ). |
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Answer» 2 tan ^-1( cosx)= tan^-1( 2cosecx); solving 2 tan^-1( cosx); we know that 2 tan^-1x= tan^-1 2x/1-x^2; replacing x with cosx 2 tan^-1( cosx)=tan^-1 2cosx/ 1- cosx^2= = tan^-1(2cosx/ sinx); 2 tan^-1( cosx)= = tan^-1(2cos x/ sinx^2) =2 cosx/ sinx^2=2 cosecx cosx/ sinx^2= cosecx cosx/ sinx^2=1/ sinx cosx= sinx^2/sinx = cosx= sinx sinx/ cosx=1 |
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