Question

Ai giúp em giải bài vd2 với ạ :(((

Answer 1

\(sin^2\alpha+cos^2\alpha=1\)

=>\(cos^2\alpha=1-sin^2\alpha=1-\left(\dfrac{4}{5}\right)^2=\dfrac{9}{25}\)

mà \(cos\alpha< 0\left(\dfrac{\Omega}{2}< \alpha< \Omega\right)\)

nên \(cos\alpha=-\sqrt{\dfrac{9}{25}}=-\dfrac{3}{5}\)

a: \(sin\left(13\Omega-\alpha\right)\)
\(=sin\left(13\Omega\right)\cdot cos\left(\alpha\right)-cos\left(13\Omega\right)\cdot sin\alpha\)

\(=0\cdot cos\alpha-\left(-1\right)\cdot\dfrac{4}{5}=\dfrac{4}{5}\)

b: \(sin\left(\dfrac{17\Omega}{2}-\alpha\right)\)

\(=sin\left(\dfrac{17}{2}\Omega\right)\cdot cos\alpha-cos\left(\dfrac{17}{2}\Omega\right)\cdot sin\alpha\)

\(=1\cdot\dfrac{-3}{5}=-\dfrac{3}{5}\)

c: \(cos\left(\dfrac{19}{2}\Omega-\alpha\right)=cos\left(\dfrac{19}{2}\Omega\right)\cdot cos\alpha+sin\left(\dfrac{19}{2}\Omega\right)\cdot sin\alpha\)

\(=0\cdot cos\alpha+\left(-1\right)\cdot\dfrac{4}{5}=-\dfrac{4}{5}\)