InterviewSolution
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InterviewSolution
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`tan^(-1)""(cosx)/(1-sinx),-(-3pi)/(2) lt x lt (pi)/(2)` , को सरलता रूप में व्यक्त कीजिए । |
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Answer» We have, LHS `=tan^(-1)(cosx)/(1-sinx)` `=tan^(-1){(sin(pi/2-x))/(1-cos(pi/2-x))}` `=tan^(-1){(2sin(pi/4-x/2)cos(pi/4-x/2))/(2sin^(2)(pi/4-x/2)}` `tan^(-1){cot(pi/4-x/2)}=tan^(-1)[tan{pi/4-x/2)}]` `=tan^(-1){tan(pi/4+x/2)}` `=(pi/4+x/2)`=RHS. Hence, `tan^(-1)(cosx)/(1-sinx)=(pi/4+2/x)`. |
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