Question

in triangle ABC angle C=90°.if tanA=1÷root3.find the value of sinA cosB+cosA×sinB​

Answer 1

In triangle ABC Angle C = 90.

Since

$\tan(a) = \frac{1}{ \sqrt{3} }$

But tan30=1/√3

=> A=30°

Since In a triangle sum of all angles is 180°.

Therefore,

A+B+C=180°

=>30°+B+90°=180°

B=60°

Now

SinACosB+CosASinB=Sin30 Cos60 + Cos30 Sin60

$\frac{1}{2} \times \frac{1}{2} + \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{3} }{2} \\ = \frac{1}{4} + \frac{3}{4} = \frac{4}{4} \\ = 1$

Hope it is helpful