Test Index

UPSC NDA 2 2019 Mathematics Solved Paper

© examsnet.com

Question : 66 of 120

Marks: +1, -0

What is cos 80° + cos 40° - cos 20° equal to?

2
1
0
$-19$

Solution:

Concept:

Use the sum-to-product identity:

\cos A + \cos B = 2 \cos \frac{A+B}{2} \cos \frac{A-B}{2}

.

Explanation:

Apply the identity to

\cos 80^\circ + \cos 40^\circ

.

Here

A = 80^\circ

,

B = 40^\circ

.

Then

\frac{A+B}{2} = \frac{80^\circ+40^\circ}{2} = 60^\circ

and

\frac{A-B}{2} = \frac{80^\circ-40^\circ}{2} = 20^\circ

.

So

\cos 80^\circ + \cos 40^\circ = 2 \cos 60^\circ \cos 20^\circ = 2 \cdot \frac12 \cdot \cos 20^\circ = \cos 20^\circ

.

Now substitute into the given expression:

\cos 80^\circ + \cos 40^\circ - \cos 20^\circ = \cos 20^\circ - \cos 20^\circ = 0

.

Answer:

0

(Option C).

© examsnet.com

Go to Question:

Prev Question

Next Question