Question

If sin (A+B) = Sin A CosB + Cos A SinB and Cos (A-B) = Cos ACosB + SinA SinB then find the values of i) Sin 120 ii) Cos 15

Answer 1

we have to find the value of 

sin 15° and cos 15° = ? 

solution:-

we know that

sin(A-B)=sinAcosB-cosAsinB

and

 cos(A-B)=cosAcosB+sinAsinB

now,

(1) sin 15° = sin ( 45° - 30°)

= sin 45°cos 30° - cos 45° sin 30°

=1/√2 × √3/2 - 1/√2 × 1/2

= √3 / 2√2 - 1 / 2√2

= ( √3 - 1) / 2√2 answer 

(2) cos 15° = cos(45° - 30°)

= cos 45° cos 30° + sin 45° sin 30°

= 1 / 2√2 × √3 / 2  + 1 / √2 × 1 / 2

= √3 / 2√2 + 1 / 2√2 

= ( √3 + 1) / 2√2 answer

✰✰ hope it helps ✰✰ 

Answer 2

Given:

"sin (A-B) = sinA cosB - cosA sinB"

"cos (A-B) = cosA cosB + sinA sin B"

To find:

The value of

Answer:

Given that

Sin (A-B) =SinA CosB - CosA SinB

Cos (A-B) =CosA CosB + SinA SinB

We need to find the

and

refer attachment for method

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