Question

show that 2cos^2theta- 1= Cos theta - Sin theta​

Answer 1

Answer:

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

Step-by-step explanation:

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