Question

How do you prove `cos^2β-sin^2β=2cos^2β-1`?

Answer 1

See proof below

Explanation:

Consider LHS as follows

`LHS=\cos^2\beta-\sin^2\beta`

`=\cos^2\beta-(1-\cos^2\beta)`

`=\cos^2\beta-1+\cos^2\beta`

`=2\cos^2\beta-1`

`=RHS`

Proved.

Answer 2

`"see explanation"`

Explanation:

`"using the "color(blue)"trigonometric identity"`

`•color(white)(x)sin^2beta+cos^2beta=1`

`"consider the left side"`

`cos^2beta-(1-cos^2beta)`

`=cos^2beta-1+cos^2beta`

`=2cos^2beta-1=" right side "rArr"verified"`