In △ABC, right-angled at B, if cot A = 1/2 , then the value of [Image] is:

In △ABC, right-angled at B, if cot A = 1/2 , then the…

In △ABC, right-angled at B, if cot A = $\frac{1}{2}$ , then the value of is:

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. -3

Cot A = $\frac{1}{2}$ = B/P

Hypotenuse = $\sqrt{2^2 + 1^2}$ = $\sqrt{5}$ .

Sin A = 2/ $\sqrt{5}$

Cos C = 2/ $\sqrt{5}$

Sin C = 1/ $\sqrt{5}$ .

Cos A = 1/ $\sqrt{5}$ .

= [2/ $\sqrt{5}$ (2/ $\sqrt{5}$ + 1/ $\sqrt{5}$ )]/[2/ $\sqrt{5}$ (1/ $\sqrt{5}$ - 2/ $\sqrt{5}$ )]

= (6/5)/(-2/5)

= -3.