Question

FIND THE VALUE OF 1-COS THETA

Answer 1

Answer:

your answer attached in the photo

Answer 2

Concept:

We will require the concept of trigonometry.

Trigonometry is the branch of mathematics that deals with the study of sides and angles of mathematical figures using functions like cosine, sine, tangent and cot etc

Formula required:

cos A-cos B=2{sin(A+B)/2}.{sin(B-A)/2}

Given:

We are given the trigonometric expression as 1-cos $\Theta$

To find:

We are asked to find the value of the given expression

Solution:

From the trigonometric formulas, we have:

cos 0°=1

Putting this value in the expression given in the question, we have:

1- cos $\Theta$

=cos 0° - cos $\Theta$ (since cos 0°=1 )

=2{sin(0+$\Theta$)/2}.{sin($\Theta$-0)/2} (Using the formula mentioned in the concept part)

=2sin$\Theta$/2. sin$\Theta$/2.

=2 sin²$\theta/2$

Hence,

1- cos $\Theta$=2 sin²$\theta/2$