Question

[Os. Htt]

1. CMR cos^2.(a-b) - sin^2.(a+b) = cos2a.cos2b

2. CMR nếu tam giá ABC tm sinA=\(\dfrac{c\text{os}B+c\text{os}C}{sinB+sinC}\) thì tg ABC vuông

Answer 1

[Mysterious Person]

a) ta có : \(cos^2\left(a-b\right)-sin^2\left(a+b\right)\)

\(=\left(cosa.cosb+sina.sinb\right)^2-\left(sina.cosb+sinb.cosa\right)^2\)

\(=cos^2a.cos^2b+sin^2a.sin^2b-sin^2a.cos^2b-sin^2b.cos^2a\)

\(=cos^2a.cos^2b-sin^2a.cos^2b+sin^2a.sin^2b-sin^2b.cos^2a\)

\(=cos^2b\left(cos^2a-sin^2a\right)-sin^2b\left(cos^2a-sin^2a\right)\)

\(=\left(cos^2b-sin^2b\right)\left(cos^2a-sin^2a\right)=cos2a.cos2b\left(đpcm\right)\)