Question

if cos2x+2cosx=1 then sin^2x (2-cos^2x) is equal to​

Answer 1

Given:

cos2x+2cosx=1

To Find:

the value of sin^2x (2-cos^2x)

Solution:

1) We will use the approach of the hit and trial to solve this question that would be the easy one.

2) We will guess  the value of the x for which the  cos2x+2cosx=1, x satisfies this equation.

3) let take the value of x is 90°

• cos180°+2cos90°
• 1 + 2×0

• 1

equal to RHS

4) Now put this value of x in given equation and find the value.

• sin²x (2-cos²x)

• sin²90° (2-cos²90°)

• 1(2 - 0)

• 2

sin²x (2-cos²x)=2