Question

sin theta = 1 by 2 ,evaluate 3 sin theta - 4 cos cube theta​

Answer 1

ans is 3(1-root 3) /2

check explanation in the pic

Answer 2

So let's begin,

sin theta = 1/2

so first of all we need to find the value of cos theta, it's quite easy just apply the appropriate formula like this:

Sin² theta + cos² theta = 1

=> ( 1/2 )² + cos² theta = 1

=> 1/4 + cos² theta = 1

=> cos² theta = 1 - 1/4

=> cos² theta = 4 - 1

4

=> cos² theta = 3/4

[ : . sin² theta + cos² theta = 1 ]

therefore, cos theta = √ 3/4 = √3/2

evaluate:

3 sin theta - 4 cos³ theta

= 3 × 1/2 - 4 × ( √3/2 )³

= 3/2 - 4 × 3√3/8

= 3/2 - 3√3/2. [ cancel +3 and -3 ]

= √3/2 × √3/√3 [ rationalize by √3 both the numerator and denominator ]

= 3/2√3

Hope it maybe helpful!!