How can I prove the identity for cos(x+pi)=-cos x ?

Question

Using the angle sum and angle difference formulas

3874 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-04T22:33:01

Using the angle addition formula for cosine.

The angle addition formula for cosine is
#cos(alpha+beta)=cosalphacosbeta-sinalphasinbeta#, and we can use this to prove that #cos(pi+x)=-cos(x)#.

#cos(pi+x)=cospicosx-sinpisinx=(cosx*-1)-(sinx*0)=-cosx#.