Question

"Question35
If A = 60° and B = 30° , verify that : sin (A + B) = sinA cos B + cos A sin B.
Chapter6,T-Ratios of particular angles Exercise -6 ,Page number 289"

Answer 1

Hey there! Thanka for the question!

Given,
A = 60° , B = 30°

Now,
sin(A + B) = sinA cos B + cos A sin B.

Substituting A = 60 , B = 30°

sin(60 +30 ) = sin60cos30+ cos 60sin 30



We know, Trigonometry ratios of particular angles : sin90 = 1 , sin30 = 1/2 , sin60 = √3/2 , cos30 = √3/2 , cos60 = 1/2

sin90 = √3/2 ( √3/2 ) + 1/2 ( 1/2 )

1 = 3/4 + 1/4

1 = 4/4

1 = 1

Both Sides of the equation are equal.

Hence, We proved and verified that sin(A + B) = sinA cos B + cos A sin B. holds good for A = 60, B = 30°

Answer 2

Hey mate !!

Here's your answer !!

Given :

A = 60° , B = 30°

To verify :

Sin ( A + B ) = Sin A . Cos B + Cos A . Sin B

Proof :

We know the values of A and B, Hence substitute them in the equation.

= Sin ( 60 + 30 ) = Sin 60 . Cos 30 + Cos 60 . Sin 30

We know the values of:

Sin 90 = 1

Sin 60 = √ 3 / 2

Cos 60 = 1 / 2

Sin 30 = 1 / 2

Cos 30 = √ 3 / 2

Hence substitute them in the below equation. We get,

= Sin 90 = Sin 60 . Cos 30 + Cos 60 . Sin 30

=> 1 = √ 3 / 2 * √ 3 / 2 + 1 / 2 * 1 / 2

=> 1 = 3 / 4 + 1/ 4

=> 1 = 1

Hence LHS = RHS.

Hence verified 

Hope it helps you mate !!

Cheers !!