Correct Answer - Option 3 : 1/12
Given
3 sin2 30° + 2 cos2 45° - 5 tan2 30°
Concept used
sin 30° = 1/2
Cos 45° = 1/√2
Tan 30° = 1/√3
Calculation
3 sin2 30° + 2 cos2 45° - 5 tan2 30°
⇒ \(3\left( {\frac{1}{4}} \right) + 2\left( {\frac{1}{2}} \right) - 5\left( {\frac{1}{3}} \right)\)
⇒ \(\frac{3}{4} + 1 - \frac{5}{3}\)
⇒ \(\frac{7}{4} - \frac{5}{3}\)
⇒ \(\frac{{21\ -\ 20}}{{12}}\)
∴ Ans = 1/12
