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

2 Answers
Harish Chandra Rajpoot
Jul 27, 2018

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.

Jim G.
Jul 27, 2018

#"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"#

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