Question

"Question20
Chapter6,T-Ratios of particular angles Exercise -6 ,Page number 288
Verify, cos60° cos30° + sin60° sin30° = cos30°"

Answer 1

Hey there!
Many of us think that, We should apply the formula of cos(A - B) here, But as we are verifying the property. We should substitute values of Trigonometry ratios.

We know that,
sin60 = √3/2
cos30 = √3/2
cos60 = 1/2
sin30 = 1/2

Now,
Taking The Left Hand side,

= cos 60° cos30° + sin60° sin30°

= √3/2 ( 1/2 ) + 1/2 ( √3/2 )

= √3/4 + √3/4

= 2√3/4

= √3/2

Taking R. H. S,
cos30

= √3/2

Therefore ,We see that L. H. S = R. H. S

Hence We proved that, cos60° cos30° + sin60° sin30° = cos30 .

Answer 2

HELLO DEAR,

we know that:-

cos(A - B) = cosAcosB + sinAsinB-------(1)

cos60° cos30° + sin60° sin30° -----(2)

on comparing----(1) & ----(2)

we get,

cos(60° - 30°)

= cos30° = √3/2
R.H.S,

L.H.S=>

cos30° = √3/2


HENCE,

R.H.S = L.H.S

we can also verify by putting values

cos60° cos30° + sin60° sin30°

= 1/2 * √3/2 + √3/2 * 1/2

= √3/4 + √3/4

= 2√3/4

= √3/2 ( R.H.S)

now ,

L.H.S =>

cos30° = √3/2



I HOPE ITS HELP YOU DEAR,
THANKS