Question

In a ΔABC, it is given that ∠C = 90° and tan A = 1/√3, find the value of

(sin A cos B + cos A sin B).

(A) 1

(B) 1/2

(C) 0

(D) 3

Answer 1

The option A is OK

Explanation

A+B+C=180°

=>A+B+90°=180°

=>B=90°-A

Now

sinAcosB+cosAsinB

=sinAcos(90°-A)+cosAsin(90°-A)

=sinA×sinA+cosA×cosA

=sin^2A+cos^2A=1

Answer 2

The correct option is: (A) 1

Explanation:

Consider ΔABC in which ∠C = 90° and tan A = 1/√3

Let BC= x

Then, AC = √3x

By Pythagoras theorem, we have