Question

Cho \(sina=\frac{2}{3}\), \(tan\left(\frac{5\pi}{2}-b\right)=\frac{3}{4}\) và a,b là các góc nhọn. Tính

a) \(A=sin\left(a+b\right)\)

b) \(B=cos\left(a-b\right)\)

Answer 1

\(cosa=\sqrt{1-sin^2a}=\frac{\sqrt{5}}{3}\)

\(tan\left(\frac{5\pi}{2}-b\right)=tan\left(2\pi+\frac{\pi}{2}-b\right)=tan\left(\frac{\pi}{2}-b\right)=cotb\)

\(\Rightarrow cotb=\frac{3}{4}\Rightarrow sinb=\frac{1}{\sqrt{1+cot^2b}}=\frac{4}{5}\)

\(\Rightarrow cosb=\sqrt{1-sin^2b}=\frac{3}{5}\)

\(A=sina.cosb+cosa.sinb=...\)

\(B=cosa.cosb+sina.sinb=...\)