In △ABC, right-angled at B, if tan A = 1/2 , then the value of (sinA(cosC+cosA))/(cosC(sinC-sinA) is:

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

In △ABC, right-angled at B, if tan A = $\frac{1}{2}$ , then the value of (sinA(cosC+cosA))/(cosC(sinC-sinA) is:

Show answer & explanation

Correct answer: C

Explanation

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

tan A = $\frac{1}{2}$ = p/b

Hypotenuse = $\sqrt{2^2 + 1^2} = \sqrt5$ .

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

Sin C = 2/ $\sqrt{5}$ .

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

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

Put the respective values, we get,

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

= 3.