COMEDK · Maths · 8. Trigonometric Ratios & Identities
The expression \(\dfrac{\tan A}{1-\cot A}+\dfrac{\cot A}{1-\tan A}\) can be written as
- A \(\sin A \cos A+1\)
- B \(\sec A \operatorname{cosec} A+1\)
- C \(\tan A+\cot A\)
- D \(\sec A+\operatorname{cosec} A\)
Answer & Solution
Correct Answer
(B) \(\sec A \operatorname{cosec} A+1\)
Step-by-step Solution
Detailed explanation
Let the expression be \(E = \dfrac{\tan A}{1-\cot A} + \dfrac{\cot A}{1-\tan A}\). Substituting \(\cot A = \dfrac{1}{\tan A}\) into the expression: \(E = \dfrac{\tan A}{1-\dfrac{1}{\tan A}} + \dfrac{\dfrac{1}{\tan A}}{1-\tan A}\)…
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