Question

in∆ABC,right angled at C if tan A=1/√3 find the value of sinA. cosB+cosA.sinB ​

Answer 1

Answer:

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

1/√3

Solution = tan A = 1/√3

tanA = 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

Answer 2

☢ AnSwer:

• The value of sin A cos B + cos A sin B = 1

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✒ GiVen :

• tan A = 1/√3

✒ To Find :

• We need to find the value of sin A cos B + cos A sin B

✒ SoluTion :

As we know that,

$\implies$tan 30° = 1 / √3

• A = 30
• C = 90 (given)

Now,

$\implies$A + B + C = 180

$\implies$30 +B + 90 = 180

$\implies$B = 180 - 120

$\implies$B = 60

Now,

$\implies$sinA cosB + cos AsinB

$\implies$sin(A + B)

$\implies$sin(30°+60°)

$\implies$sin90°

$\implies$1

Therefore, value of sin A cos B + cos A sin B is 1.

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