Question

Find the value of sin ³a ? (if it is given that sin²a +cos²a = 1 )​

Answer 1

ANSWER:

${(1 - { \cos }^{2} a)}^{ \frac{3}{2} }$

GIVEN:

sin² a + cos² a = 1

TO FIND:

sin ³ a = ??

FORMULAE:

$x^m \times x^n = x^{m + n}$

sin² a = 1 - cos² a

$\sin a = \sqrt{1 - { \cos}^{2}a }$

EXPLANATION:

sin³ a = sin a (sin² a)

${ \sin}^{3} a = (1 - { \cos}^{2} a) \sqrt{(1 - { \cos}^{2} a)}$

${ \sin}^{3} a = {(1 - { \cos}^{2} a)}^{1 + \frac{1}{2} }$

$1 + \frac{ 1 }{2} = \frac{3}{2}$

${ \sin}^{3} a = {(1 - { \cos}^{2} a)}^{ \frac{3}{2} }$