Question

If cos+cos^2 =1 then find the value of sin^2+sin^4

Answer 1

The value of
`sin^(2)x + sin^(4)x` is 1

Explanation:

Given as :

cos x + cos² x = 1

So,
`sin^(2)x + sin^(4)x` = sin²x + (sin²x)²

Or,
`sin^(2)x + sin^(4)x` = sin²x + (1 - cos²x)²

AS given in question that cos x + cos² x = 1

I.e cox = 1 - cos²x

So,
`sin^(2)x + sin^(4)x` = sin²x + cos²x

∵ Note: sin²x + cos²x = 1

∴
`sin^(2)x + sin^(4)x` = 1

Hence the value of
`sin^(2)x + sin^(4)x` is 1 Answer