SSC CGL 2023 PYQ — Question 57

The correct answer is Option 1 i.e. $\frac{2}{ 3}$.

$\frac{4}{3}$ tan² 45° + 3 cos² 30° - 2 sec² 30° - $\frac{3}{4}$  cot² 60°

On putting the values of trigonometric ratios

⇒ tan 45° = 1

⇒ cos 30° = √3/2

⇒ cot 60° = 1/√3

Now,

⇒ $\frac{4}{3} \times (1)^2 + 3\times({\sqrt3\over2})^2 - 2\times ({2\over\sqrt3})^2 - {3\over4} \times ({1\over\sqrt3})^2$

⇒ $\frac{4}{3} + 3\times({3\over4}) - 2\times ({4\over3}) - {3\over4} \times ({1\over3})$

⇒ $\frac{4}{3} + ({9\over4}) - ({8\over3}) - {1\over4}​​$

⇒ $\frac{16}{12} + ({27\over12}) - ({32\over12}) - {3\over12}$ = $8\over12$ = $\frac{2}{ 3}$