Question

If triangle ABC right angle at C if tan A =1/root3 find the value of sin A cosB+ cos A sin B

Answer 1

"The value of$\sin A \cos B + \cos A \sin B = 1$

Given:

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

To find:

$Value of \sin A \cos B + \cos A \sin B$

Solution:

In the given right angled triangle

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

Since $\tan 30 ^ { \circ} = \frac { 1 } { \sqrt { 3 } }$

A = 30

Given C = 90

So, “A” + “B” + “C” = “180”

or,  “B = 60”

Hence, $\tan B = \tan 60 ^ { \circ} = \sqrt { 3 }$

B = 60

Now, $\sin A \cos B + \cos A \sin B = \sin ( A + B ) = \sin \left( 30 ^ { \circ} + 60 ^ { \circ} \right) = \sin 90 ^ { \circ} = 1$

Hence, the value will be 1."

Answer 2

Given - ABC is a right angled triangle , tan A =

$\frac{1}{ \sqrt{3} }$

Solution -

tan A =

$\frac{1}{ \sqrt{3} }$

tan A = tan 30° ( tan 30° = 1/√3 )

A = 30°

C = 90° (Given)

So, Therefore , B = 90 - 30 = 60°(Angle sum property of a triangle / A + B + C = 180° )

Sin A • Cos B + Cos A • Sin B

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