Question

2sin²π/6+cosec²7π/6cos²π/3=3/2

Answer 1

hey mate here is ur Ans

we know that sin(π/6)=1/2
cosec(7π/6)=cosec(π+π/6)=-cosec(π/6)=-2
and. cos(π/3)=1/2

so,. 2(1/2)²+(-2)² (1/2)²

(2/4)+4(1/4)
2/4+1
1/2+1
3/2

Answer 2

$\huge \color{red}{ \boxed {\boxed{ \bf{Answer}}}}$

$\large { \underline{ \underline{\bold{Given:}}}}$

$2 {sin}^{2} \: \frac{\pi}{6} + {cosec}^{2} \: \frac{7\pi}{6} \times {cos}^{2} \: \frac{\pi}{3} = \frac{3}{2}$

$\large { \underline{ \underline{\bold{To \: find:}}}}$

It's verification

$\large { \underline{ \underline{\bold{Solution:}}}}$

We know that value of π in trigonometry is 180°

$\frac{\pi}{6} = \frac{ \cancel{180}}{ \cancel6} {}^{ {}^{30} } = 30 \degree$

$\frac{7\pi}{6} = \frac{ 7 \times \cancel{180}}{ \cancel6} {}^{ {}^{30} } =7 \times 30 = 210 \degree$