Question

$\frac{sin(A+B)}{cosAcosB}=tanA+tanB$
If true then enter $1$ and if false then enter $0$

Answer 1

Given: $A={60}^{\circ }$, $B={30}^{\circ }$
Now, $\frac{sin(A+B)}{cosAcosB}=tanA+tanB$
L.H.S = $\frac{sin({60}^0+{30}^0)}{cos{60}^{0}cos{30}^0}$
= $\frac{sin{90}^0}{cos{60}^0\cos {30}^0}$
= $\frac{1}{\frac{\sqrt{3}}{2}.\frac{1}{2}}$
= $\frac{4}{\sqrt{3}}$
R.H.S: $\tan {60}^0+\tan {30}^0$
= $\sqrt{3}+\frac{1}{\sqrt{3}}$
= $\frac{3+1}{\sqrt{3}}$
= $\frac{4}{\sqrt{3}}$