Question

"Question9
Evaluate, cos60° cos30° - sin60° sin30°
Chapter6, Trigonometry, Exercise-6, Page number 288"

Answer 1

Hey there!

We know that , cos( A + B ) = cosA cos B - sinA sinB.

So, cos60° cos30° - sin60° sin30° is in the form of cosA cos B - sinA sinB. .

Now,

cos60° cos30° - sin60° sin30°

= cos ( 60+30)

= cos 90

We know that, cos90° = 0

= 0

[ or ]

We know trigonometric ratios of special angles : cos60 = sin30 = 1/2 , cos30 = sin60= √3/2

= cos60° cos30° - sin60° sin30°

= 1/2 ( √3/2 ) - (√3/2 ) ( 1/2 )

= √3/4 - √3/4

= 0

Therefore ,cos60° cos30° - sin60° sin30° = 0

Hope helped!

Answer 2

HELLO DEAR,


We know that ,


cos( A + B ) = cosA cos B - sinA sinB.

NOW,


cos60° cos30° - sin60° sin30°

= cos ( 60+30)

= cos 90
[ cos90° = 0 ]

= 0



another method,


We know that:-

cos60 = sin30 = 1/2 ,
cos30 = sin60= √3/2

= cos60° cos30° - sin60° sin30°

= 1/2 ( √3/2 ) - (√3/2 ) ( 1/2 )

= √3/4 - √3/4

= 0




I HOPE ITS HELP YOU DEAR,
THANKS