Question

costheta + cos(π+ theta )+ cos(2π+ theta) + ...+ cos(20π + theta)

Answer 1

Given: The trigonometric terms cos theta + cos(π+ theta )+ cos(2π+ theta) + ...+ cos(20π + theta)

To find: The value of the given term.

Solution:

• Now we have given the term as :

               cos theta + cos(π+ theta )+ cos(2π+ theta) + ...+ cos(20π + theta)

• Now we know that cos (  π+ theta ) = - cos theta

• Also cos (2π+ theta) = cos theta

• Similarly cos ( 3 π+ theta ) = - cos theta

• So applying this, we get:

               cos theta  - cos theta + cos theta - cos theta ....... + cos(20π + theta)

• So the only term remaining will be:

               cos(20π + theta) = cos theta.

               cos theta.

Answer:

                 So the value of the given term is cos theta.

Answer 2

the answer is cos theta