JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
The expression\(\frac{{\tan A}}{{1 - \cot A}} + \frac{{\cot A}}{{1 - tanA}}\) can be written as:
- A \(\sin A\cos A + 1\)
- B \(\sec A cosecA + 1\)
- C \(\tan A + \cot A\)
- D \(\sec A + cosec\;A\)
Answer & Solution
Correct Answer
(B) \(\sec A cosecA + 1\)
Step-by-step Solution
Detailed explanation
\( = \frac{{\sin A}}{{\cos A}} \times \frac{{\sin A}}{{\sin A - \cos A}} + \frac{{\cos A}}{{\sin A}} \times \frac{{\cos A}}{{\cos A - \sin A}}\) \( = \frac{1}{{\sin A - \cos A}}\left\{ {\frac{{{{\sin }^3}A - {{\cos }^3}A}}{{\cos A\sin A}}} \right\}\)…
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