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InterviewSolution
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सरलतम रूप व्यक्त कीजिए - `tan^(-1)((cosx)/(1-sinx))` |
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Answer» यहाँ `tan^(-1)((cosx)/(1-sinx))` `=tan^(-1){(cos^(2).(x)/(2)-sin^(2).(x)/(2))/(cos^(2).(x)/(2)+sin^(2).(x)/(2)-sin.(x)/(2)cos.(x)/(2))}` `=tan^(-1){((cos.(x)/(2)+sin.(x)/(2))(cos.(x)/(2)-sin.(x)/(2)))/((cos.(x)/(2)-sin.(x)/(2))^(2))}` `=tan^(-1){((cos.(x)/(2)+sin.(x)/(2)))/((cos.(x)/(2)-sin.(x)/(2)))}` `=tan^(-1){(1+tan.(x)/(2))/(1-tan.(x)/(2))}` `=tan^(-1){tan((pi)/(4)+(x)/(2))}` `=(pi)/(4)+(x)/(2)`जो कि अभीष्ट सरलतम रूप है। |
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