Question

The value of tan2 30° - 3 sin2 60° +
cosec2 45° is
8
12
None of these​

Answer 1

tan[2(30°)] - 3 sin[2(60°)] + cosec[2(45°)]

tan(60) - 3 sin(120) + csc(90)

Sin(120) is nothing but sin(90 + 30)

Sin (90+x) is second quadrant which is +ve of sin and since it is 90+, we change the trigonometric term to cos.

So, Sin(90+x) is cos(x)

So, our equation ends up as,

tan(60) - 3 cos(30) + csc(90)

$\sqrt{3}$ - 3($\sqrt{3} /2$) + 1

[2$\sqrt{3}$ - 3$\sqrt{3}$ + 2] / 2

[$\sqrt{3}$ + 2] / 2

So the answer is [$\sqrt{3}$ + 2] / 2 , none of these.