Question

Find the value of cos^2 15 +cos^2 45+ cos^2 75


please give me the answer​

Answer 1

Answer:

Your ans is as follows

Step-by-step explanation:

we know that 1 + cos 2theta = 2 cos^2 theta

hence, cos^2 theta =( 1 + cos 2theta)/2

Hence,

cos^2 15 + cos^2 45 + cos^2 75

= 1 + cos 2(15) + 1 + cos 2(45) + 1 + cos 2(75)

= 1 + cos 30 + 1 + cos 90 + 1 + cos 150

= 1 +

$\sqrt{3} \div 2$

+ 1 + 0 + 1 +

$\sqrt{3} \div 2$

.........................(as cos 150 = cos ( 180 - 30) = -cos 30 = cos 30)

3 +

$2 \sqrt{3} \div 2$

If you solve further you will get final ans as

$2 \sqrt{3}$

Hope this helps you