Question

sin raised to 4 theta + Cos raise to 4 theta is equals to 1 - 2 sin square theta cos square theta​

Answer 1

Answer:

${ \sin( \alpha ) }^{4} + { \cos( \alpha ) }^{4} \\ = {{( \sin( \alpha ) }^{2} )}^{2} + {{( \ \cos( \alpha ) }^{2} )}^{2} \\ = {{( \sin( \alpha ) }^{2} )}^{2} + {{( \ \cos( \alpha ) }^{2} )}^{2} + 2 { \sin( \alpha ) }^{2} { \cos( \alpha ) }^{2} - 2 { \sin( \alpha ) }^{2} { \cos( \alpha ) }^{2} \\ = {( { \sin( \alpha ) }^{2} + { \cos( \alpha ) }^{2} )}^{2} - 2 { \sin( \alpha ) }^{2} { \cos( \alpha ) }^{2} \\ = 1 - 2 { \sin( \alpha ) }^{2} { \cos( \alpha ) }^{2}$

Answer 2

Step-by-step explanation:

sin(α)4+cos(α) 4

=(sin(α) 2 ) 2 +( cos(α) 2 ) 2

=(sin(α) 2 ) 2 +( cos(α) 2 )2+2sin(α)2cos(α)2−2sin(α) 2 cos(α) 2

=(sin(α) 2 +cos(α) 2 ) 2 −2sin(α) 2 cos(α) 2

=1−2sin(α) 2 cos(α) 2