$\sqrt{\frac{1+sinA}{1-sinA}}$= _______.

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

$\sqrt{\frac{1+sinA}{1-sinA}}$= _______.

Options:

cosec A - cot A

sec A - tan A

sec A + tan A

sec A

Correct Answer:

sec A + tan A

Explanation:

$\sqrt{\frac{1+sinA}{1-sinA}}$

Multiply and divide by ( 1 + sinA )

= $\sqrt{\frac{1+sinA}{1-sinA}}$ × $\sqrt{\frac{1+sinA}{1+sinA}}$

= $\sqrt{\frac{(1+sinA)²}{cos²A}}$

= $\frac{( 1 + sinA ) }{cosA}$

= secA + tanA