Question 20
a) Simplify
$$\left(\frac{\cos\alpha}{\cos\beta}\right)^2-(\cos\alpha\tan\beta)^2+\sin^2\alpha$$
when $\cos\beta\ne0$.
b) Find $\alpha+\beta$ without a calculator if $\sin\alpha=\sqrt5/5$, $\sin\beta=\sqrt{10}/10$ and $0^\circ\lt\alpha,\beta\lt45^\circ$.
$$\left(\frac{\cos\alpha}{\cos\beta}\right)^2-(\cos\alpha\tan\beta)^2+\sin^2\alpha$$
when $\cos\beta\ne0$.
b) Find $\alpha+\beta$ without a calculator if $\sin\alpha=\sqrt5/5$, $\sin\beta=\sqrt{10}/10$ and $0^\circ\lt\alpha,\beta\lt45^\circ$.