Question

In a triangle abc right angle at c .If tan A 1/√3 find the value of sin A× cos B + cos A × sin B .

Answer 1

Answer is 1. View the solution

Answer 2

sin A × cos B + cos A × sin B  = 1

Step-by-step explanation:

Given:

Δ ABC is a Right Triangle at ∠C = 90°

$\tan A=\dfrac{1}{\sqrt{3}}$

To Find:

sin A × cos B + cos A × sin B = ?

Solution:

Δ ABC is a Right Triangle at ∠C = 90° .......Given

$\tan A=\dfrac{1}{\sqrt{3}}$

Also

$\tan 30=\dfrac{1}{\sqrt{3}}$

Therefore,

∠ A = 30°

Now in ΔABC

$\angle A + \angle B + \angle C = 180\°$ .........angle sum Triangle property

substituting the values we get

$\angle B=180-90-30=60\°$

$\angle B=60\°$

So the value of

sin A × cos B + cos A × sin B  = $\sin 30\times \cos 60 +\cos 30\times \sin 60 \\=\dfrac{1}{2}\times \dfrac{1}{2}+ \dfrac{\sqrt{3} }{2}\times \dfrac{\sqrt{3} }{2} \\=\dfrac{1}{4}+\dfrac{3}{4}\\=\dfrac{4}{4}\\=1$

Therefore

sin A × cos B + cos A × sin B  = 1