The expression \frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}

Correct Answer is : secAcosecA+1

NIMCET 2020 Question Paper with solutions

Question : 44 of 120

Marks: +1, -0

The expression

{\tan A}/{1-\cot A}+{\cot A}/{1-\tan A}

Solution:

{\sin x}/{\cos(1-\cos{/}\sin x)}+{\cos x}/{\sin x(1-\sin x{/}\cos x)}

⇒{\sin^2 x}/{\cos x(\sin x-\cos x)}+{\cos^2 x}/{\sin x(\cos x-\sin x)}

⇒{\sin^3 x-\cos^3x}/{\sin x\cos x(\sin x-\cos x)}

⇒{(\sin x-\cos x)(1+\sin x\cos x)}/{\sin x\cos x(\sin x-\cos x)}

⇒\sec A\cosec A+1

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