Chapter 7: Trigonometric Ratios of Compound Angles – Exercise 7.1

Trigonometric Ratios of Compound Angles – Exercise 7.1 – Q.1

We have,

Now,

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

We have, 

Now,

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

We have,

Now,

Sin (A - B) = sin A cos B - cos A sin B

We have,

Now

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

 

Trigonometric Ratios of Compound Angles – Exercise 7.1 – Q.2

We have,

Now,

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

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

We have,

Now,

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

 

Trigonometric Ratios of Compound Angles – Exercise 7.1 – Q.3

Now,

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

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

 

Trigonometric Ratios of Compound Angles – Exercise 7.1 – Q.4

We have,