Maths · Trigonometrical identities and trigonometrical functions
If for all permissible values of then belongs to This question has multiple corr
If \( \sqrt{\frac{1-\sin A}{1+\sin A}}+\frac{\sin A}{\cos A}=\frac{1}{\cos A}, \) for all permissible values of \( A, \) then \( A \) belongs to This question has multiple correct options
- A. First Quadrant
- B. Second Quadrant
- C. Third Quadrant
- D. Fourth Quadrant
Step-by-step solution
The expression simplifies to (1 - sin A)/|cos A| + sin A/cos A = 1/cos A. For cos A > 0, |cos A| = cos A, giving 1/cos A = 1/cos A, which holds for all permissible A. For cos A < 0, we get sin A = 1, which is not permissible. Thus A must be in first or fourth quadrant.
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