Question

√3 cos 13 + sin 13 = 2 sin 73 , please prove it

Answer 1

$\sqrt{3} \cos13 + \sin13 \\ = 2( \frac{ \sqrt{3} }{2} \cos13 + \frac{1}{2} \sin13) \\ = 2( \sin60 \cos13 + \cos60 \sin13) \\ = 2 \sin(60 + 13) = 2 \sin73$

Answer 2

Answer:

Step-by-step explanation:

LHS: $\sqrt{3}cos13+sin13$

Multiplying and dividing by 2, we have

=$2(\frac{\sqrt{3}}{2}cos13+\frac{1}{2}sin13)$

Using $sin60=\frac{\sqrt{3}}{2}$ and $cos60=\frac{1}{2}$, we get

=$2(sin60cos13+cos60sin13)$

Using, $sin(A+B)=sinAcosB+cosAsinB$, wehave

=$2sin(60+13)$

=$2sin73$

=RHS

Hence proved.