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If A,B,C are angles of a …

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If A,B,C are angles of a triangle then prove that cosA+cos(B-C)=2sinB sinC

Posted by Priyanshi Setia 5 years, 10 months ago

CBSE > Class 11 > Mathematics

1 answers

Susai Raj 5 years, 10 months ago

We know that A + B +C = 180° (sum of 3 angles of a triangle)

So A = 180-(B+C)

Also cos(180-X) = -cos X .and

cos(X +/- Y) =cosXcosY -/+ sinXsinY.

Now cosA + cos(B-C)= cos{180-(B+C)}+cos(B-C)

=--cos(B+C)+cos(B-C)

=-(cosBcosC-sinBsinC)+cosBcosC+sinB sinC

=-cosBcosC+sinB sinc+cosBcosC+sinB sinC

=2sinBsinC.

2Thank You

ANSWER

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CBSE > Class 11 > Mathematics