Question

If sin alpha=1/2,prove that(3cos alpha-4cos^3alpha)=0

Answer 1

sin alpha=1/2,      RTP: 3cosalpha - 4 cos^3alpha = 0

Now,

since sin alpha is = 1/2

we know that

sin 30 = 1/2

so,

alpha = 30

now,

3 cos30 - 4 cos ^3 30

 => 3(root3)/2      -       4(root3/2)^3

 => 3 * root3/2    -       4(3 * root 3)/8

 => 12 *root3/8    -       12* root3/8                       [taking common denominator]

 => 0

Answer 2

Given.

$\sin \alpha = \frac{1}{2}$

To prove.

$3 \cos \alpha - 4 { \cos }^{3} \alpha = 0$

Solution.

$\sin \alpha = \frac{1}{2}$

$⇒ \sin \alpha = \sin30° \:$

$⇒ \: \alpha = 30° \:$

Now, taking LHS,

$3 \cos \alpha - 4 { \cos }^{3} \alpha = 3 \cos30° \: - 4 { \cos }^{3} 30° \:$

$= 3( \frac{ \sqrt{3} }{2}) - 4 ({ \frac{ \sqrt{3} }{2} })^{3}$

$= \frac{3 \sqrt{3} }{2} - 4( \frac{3 \sqrt{3} }{8} )$

$= \frac{3 \sqrt{3} }{2} - \frac{3 \sqrt{3} }{2}$

$= 0$

= RHS

∴ LHS = RHS

Hence, proved.

Please mark the BRAINLIEST.

CHEERS!