Question

If cos x + cos^2 x = 1, prove that sin^2x + sin^4 x = 1.​

Answer 1

Answer:

Given:

The equation is,

Cosx+cos²x=1

To prove:

Sin²x+Sin⁴x=1

Solution:

As it is given that,

Cosx+ cos²x=1

Cosx=1-cos²x

And, Take LHS from the equation,

Sin²x+Sin⁴x=1

→Sin²x+Sin⁴x

→Sin²x(1+sin²x)

→(1-cos²x)(1+1-cos²x)

→Cosx(1+cosx)

→cosx+cos²x=1

Step-by-step explanation:

Hope it helps you......