Question

cos^4 theta - sin^ 4 theta + 1 = 2 cos ^ 2 theta . prove that . ​

Answer 1

Step-by-step explanation:

cos 4 theta- sin 4theta=2cos 2 theta-1

lhs

(cos2)2theta-(sin^2)2

(cos2theta+sin^2theta)(cos^2 theta-sin2 theta)

cos 2 theta-sin2 theta

cos 2theta-1+cos2theta

2cos2 theta-1

=rhs

hence proved

Answer 2

Step-by-step explanation:

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