$({cosec} A-\cot A)(1+\cos A)=?$

CUET Preparation Today

Start Free Mocks

Home Questions QUPDEKJHU9

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

$({cosec} A-\cot A)(1+\cos A)=?$

Options:

$\cos A$

$\sin A$

$\cot A$

$cosec~A$

Correct Answer:

$\sin A$

Explanation:

( cosecA - cotA ) . ( 1 + cosA )

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

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

= $\frac{1² - cos²A}{sinA}$ )

{ using , sin²A + cos²A = 1 }

= = $\frac{sin²A}{sinA}$ )

= sinA