Question

Find the value of sin^2 pi/10 + sin^2 4pi/10 + sin^2 6pi/10 + sin^2 9pi/10.

Answer 1

Given - Trigonometric equation - sin^2 pi/10 + sin^2 4pi/10 + sin^2 6pi/10 + sin^2 9pi/10.

Find - To find the value of given trigonometric equation.

Solution - Value of pi in angles is 180 degrees

Hence, pi/10 is 18 degree, 4pi/10 is 72 degrees, 6pi/10 is 108 degrees and 9pi/10 is 162 degrees.

Keeping the values of sin as per the degree -

= sin² 18 + sin² 72 + sin² 108 + sin² 162

= 0.095 + 0.90 + 0.904 + 0.095

= 1.99

Therefore, the value of equation given in question is 1.99

Answer 2

$= \sin^{2} ( \frac{\pi}{10} ) + \sin^{2} ( \frac{4\pi}{10} ) + \sin^{2} ( \frac{6\pi}{10} ) + \sin^{2} ( \frac{9\pi}{10}$

$= \sin^{2} 18 + \sin^{2}72 + \sin^{2}108 + \sin^{2}162$

$= \sin^{2}18 + \cos^{2}18 + \sin^{2}72 + \cos^{2}72$

$= 1 + 1$

$= 2$

Hope this is helpful

please mark me as brainlist answer