Question

If sin A = √3/2, find the value of 2 cot^2 A -1.

Answer 1

Question:-

$\bf \: \sin(A) = \frac{ \sqrt{3} }{2} \: \: \: \: \: \: \: find \: the \: value \: of \: 2 \cot {}^{2} (A) - 1$

Solution:-

Given,

$\bf \: \sin(A) = \frac{ \sqrt{3} }{2}$

We have find the value of

$\bf \: 2 \cot {}^{2} (A) - 1$

Trigonometry ratio

$\bf \: \sin(A) = \frac{ \sqrt{3} }{2} = \frac{p}{h}$

$\bf \: \cot(A) = \frac{b}{p}$

Now using pythagoras

h = 2 , p = √3 , b = ?

h² = p² + b²

( 2 )² = ( √3 )² + b²

4 = 3 + b²

4 - 3 = b²

b² = 1

b = 1

Value of cot ( A ) = 1 / √3

Now put the value on

$\bf \: 2 \cot {}^{2} (A) - 1$

we get ,

$\bf \: 2 \times ( \frac{1}{ \sqrt{3} } ) {}^{2} - 1$

$\bf \: 2 \times ( \frac{1}{{3} } ) {}^{} - 1$

$\bf \: \frac{2}{3} - 1$

$\bf \frac{2 - 3}{3}$

$\bf \: \frac{ - 1}{3}$

$\boxed{ \orange{ \bf \: {Answer = \frac{ - 1}{3} }}}$