Question

If 2 cos a = √3, prove that 3 sin a - 4 sin^3
where a=1​

Answer 1

Step-by-step explanation:

2cos a = √3

cos a =√3/2

cos a =cos 30°

a = 30°

Now, substitute 30° in place of 'a'

3 sin 30° - 4( sin 30°)^3

= 3 (1/2) - 4(1/2)^3

=3/2-4(1/8)

=3/2-1/2

=3-1/2

=2/2

=1

hence proved a = 1

Answer 2

another method

cos a= √3/2 = cos30

a= 30°

now,

3 sina - 4 sin^3a

= sin3a

= sin 3*30°

= sin 90°

= 1