Question

sin30- sin 90+2cos0/tan30 tan60

Answer 1

Hello!

$\dfrac{\sf sin\:30^{\circ} - sin\:90^{\circ} + 2cos\:0^{\circ}}{\sf tan\:30^{\circ}.tan\:60^{\circ}}$

⇒ $\dfrac{\dfrac{\sf 1}{\sf 2} - 1 + 2 ( 1 )}{\dfrac{\sf 1}{\cancel{\sqrt{3}}} \sf \:x\: \cancel{\sqrt{3}}}$

⇒ $\dfrac{\sf 1 - 2 + 4}{\sf 2}$ = $\boxed{\dfrac{\sf 3}{\sf 2}}$

Cheers!

Answer 2

$\bf \large \it \: Hey \: User!!!$

first of all, lemme tell their values (trigonometric ratios) :-

$<b > • sinA at 30° = 1/ 2 and at 90° = 1$

$<b > • tanA at 30° = 1/√3 and at 60° = √3$

$<b > • cosA at 0° = 1$

$\bf given = > \frac{ \sin(30) - \sin(90) + 2 \cos(0) }{ \tan(30) \times \tan(60) } \\ \\ \bf \: = > \frac{ \frac{1}{2} - 1 + 2}{ \frac{1}{ \sqrt{3} } \times \sqrt{3} } \\ \\ \bf \: = > \frac{ \frac{1}{2} +1}{ \frac{ \sqrt{3} }{ \sqrt{3} } } \\ \\ \bf = > \frac{ \frac{1}{2} + \frac{2}{2}}{1} \\ \\ \bf \: = > \frac{ \frac{3}{2}}{1} \\ \\ \bf => \boxed{ \frac{3}{2}} \: final \: answer$

$\bf \large \it{Cheers!!!}$