Question

If sin B = 1/2. Show that 3(cos B)- 4(cos³B) = 0.

Answer 1

Hi ,

sin B = 1/2

sin B = sin 30

Therefore ,

B = 30 -----( 1 )

according to the problem given,

LHS = 3(cos B ) - 4 Cos³ B

= - ( 4cos³ B - 3 cos B )

[ since cos 3x = 4cos³ x - 3 cos x ]

= - cos 3B

= - cos ( 3 × 30) from ( 1 )

= - cos 90

= 0

= RHS

I hope this helps you.

:)

Answer 2

Hello friend

we know that 3cosB - 4cos³B =. - Cos3B
since. [4cos³x -3cosx = cos3x]
So
sinB = 1/2. { given
From this we can conclude that B = 30°

Now
-cos3(30)° = -cos90°
so => 0

hece proved