Question

Cos 4A = 1- 8cos^2 A + 8cos^4 A prove that

Answer 1

Answer:

Step-by-step explanation:

L.H.S=cos4A=cos2(2A)

=2cos  

2

2A−1

=2(2cos  

2

A−1)  

2

−1

=2(4cos  

4

A+1−4cos  

2

A)−1

=8cos  

4

A+2−8cos  

2

A−1

=8cos  

4

A−8cos  

2

A−1=R.H.S

Hence proved.

Answer 2

Step-by-step explanation:

LHS=    COS4A= 2COS²2A-1

                        = 2(2COS²A-1)²- 1

                        = 2(4COS²A+1-4COS²A) - 1

                        = 8COS⁴A+2-8COS²A - 1

                        = 1-8COS²A+8COS⁴A = RHS