Question

Cho sin α = 1/2 tính A = 3sin^a + 4cos^a

Answer 1

Lời giải:

$\cos ^2a=1-\sin ^2a=1-(\frac{1}{2})^2=\frac{3}{4}$

$\Rightarrow \cos a=\pm \frac{\sqrt{3}}{2}$

Nếu $\cos a=\frac{\sqrt{3}}{2}$ thì:

$A=3\sin a+4\cos a=3.\frac{1}{2}+4.\frac{\sqrt{3}}{2}=\frac{3+4\sqrt{3}}{2}$

Nếu $\cos a=\frac{-\sqrt{3}}{2}$ thì:

$A=3\sin a+4\cos a=3.\frac{1}{2}+4.\frac{-\sqrt{3}}{2}=\frac{3-4\sqrt{3}}{2}$