Question

if sin0+sin^20=1 find cos^20+cos^40​

Answer 1

Question :

If sin@ + (sin@)^2 = 1 ,then find the value of : (cos@)^2 + (cos@)^4.

Note:

(sin@)^2 + (cos@)^2 = 1

Or

(sin@)^2 = 1 - (cos@)^2

Solution:

Give:

sin@ + (sin@)^2 = 1 -------(1)

To find:

(cos@)^2 + (cos@)^4 = ?

We have;

=> sin@ + (sin@)^2 = 1

=> sin@ = 1 - (sin@)^2

=> sin@ = (cos@)^2 --------(2)

{ (sin@)^2 = 1 - (cos@)^2 }

Now,

Squaring both sides in eq-(1)

We get;

=> (sin@)^2 = {(cos@)^2}^2

=> (sin@)^2 = (cos@)^4 ----------(3)

Thus;

(cos@)^2 + (cos@)^4

= (sin@) + (sin@)^2 {using eq-(2),(3)}

= 1 {using eq-(1)}

Hence,

The required value of the

(cos@)^2 + (cos@)^4 is 1.