Question

If sin x = √5/3 and 0< x < π/2, find the value of cos 2x.

Answer 1

Answer:

sinx =

$\frac{p}{h}$

p = √5

h = 3

BY PYTHAGORAS THEOREM

${h}^{2} = {b}^{2} + {p}^{2}$

${3}^{2} = {b}^{2} \times { \sqrt({5}) }^{2}$

$9 - 5 = {b}^{2}$

$\sqrt{4} = b$

$b \: = 2$

Now,

0< x <π/2

0 < x < 90

therefore, x lies in 1st quadrant

where all trigonometry values are positive.

cos2x =

$\frac{2b}{h}$

$\frac{2 \times 2}{3}$

$\frac{4}{3}$ ---------answer