Question

If cod (A+B)= cos A cos B - sin A sin B, find the value of cos 75° and cos 105°.​

Answer 1

GIVEN: cos(A+B) = cosAcosB - sinAsinB

i) cos 75°

ii) cos 105°

ANSWER:

i) cos 75°

= cos(45 + 30)

= cos45.cos30 - sin45.sin30

= 1/√2 x √3/2 - 1/√2 x 1/2

= √3 / 2√2 - 1 / 2√2

= √3 - 1 / 2√2

ii) cos 105°

= cos(60 + 45)

= cos60.cos45 - sin60.sin45

= 1/2 x 1/√2 - √3/2 x 1/√2

= 1 / 2√2 - √3 / 2√2

= √3 / 2√2

Ans. : i) √3-1 / 2√2

ii) √3 / 2√2

Hope you got it,

Thanks.