Question

(cos^4) + (sin^4 ) = (3+cos4a)/4

Answer 1

Answer:

Note first that  cos4(A)−sin4(A)=cos2(A)−sin2(A) . Also  cos4(A)+sin4(A)=1−2cos2(A)sin2(A)=1−12sin2(2A) .

At points at which  sec(2A)  is defined, we can multiply both sides to the equation by  (3+cos(4A))cos(2A)  to obtain the equivalent equation

2(2−sin2(2A))cos(2A)=(cos2(A)−sin2(A))(3+cos2(2A)−sin2(2A)) .

The second factor on the right hand side is  2(1+cos2(2A))  so the question reduces to proving  (2−sin2(2A))cos(2A)=(cos2(A)−sin2(A))(1+cos2(2A)).  

The first factor on the left is equal to the second factor on the right, so we are reduced to  cos(2A)=cos2(A)−sin2(A)

Step-by-step explanation: