**Compound Angle Formula Examples :**

Here we are going to see example problems based on the formula for compound angles.

sin (x + y) = sin x cos y + cos x sin y

sin (x - y) = sin x cos y - cos x sin y

cos (x + y) = cos x cos y - sin x sin y

cos (x - y) = cos x cos y + sin x sin y

tan (x + y) = (tan x + tan y) / (1 - tan x tan y)

tan (x - y) = (tan x - tan y) / (1 + tan x tan y)

**Question 1 :**

If sin A = 3/5 and cos B = 9/41 , 0 < A < π/2, 0 < B < π/2,

find the value of (i) sin(A + B) (ii) cos(A − B).

**Solution :**

(i) sin(A + B)

Formula for sin (A + B) is sin A cos B + cos A sin B.Now we have to find the values of cos A and sin B.

sin A = 3/5
cos A = 4/5 |
cos B = 9/41
sin B = 40/41 |

sin(A + B) = sin A cos B + cos A sin B

= (3/5)** **⋅** (9/41****) + (4**/15) ⋅ (40/41)

= (27/205) + (160/205)

= (27 + 160)/205

= 187/205

Hence the value of sin (A + B) is 187/205.

(ii) cos(A − B)

Formula for cos (A - B) is cos A cos B + sin A sin B.

cos (A - B) = cos A cos B + sin A sin B.

= (4/5)** **⋅** (9/41****) + (3**/5) ⋅ (40/41)

= (36/205) + (120/205)

= (36 + 120)/205

= 156/205

Hence the value of cos (A - B) is 156/205.

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