Question

in triangle abc right angled at B if tan a = to 1 by root 3 find the value of Sin A cos C + cos a sin c

Answer 1

$tan \: a = \frac{1}{ \sqrt{3} }$
$a = {30}^{0}$
$c = {60}^{0}$
sin A cos C + cos A sin C

= sin(A+C)

= sin 90
= 1

Answer 2

Answer:

The answer is 1.

Step-by-step explanation:

Given,

ABC is a right triangle,

In which ∠B = 90°

tan A = 1/√3

⇒ ∠A = 30°

We know that,

The sum of all interior angles of a triangle is supplementary,

⇒ ∠A + ∠B + ∠C = 180°

⇒ 30° + 90° + ∠C = 180° ⇒ ∠C = 180° - 120° = 60°

Thus,

$sin A.cos C + cos A. sin C$

$=sin 30^{\circ}.cos 60^{\circ}+cos 30^{\circ}.sin 60^{\circ}$

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

$=\frac{1}{4}+\frac{3}{4}$

$=\frac{4}{4}$

$=1$