Question

if tan theta is 5 find the value of cos 2 theta​

Answer 1

if tan theta is 5 find the value of cos 2 theta...❓

⭐Solution⭐

➡Given here

Tan x = 5,

So,

Sin x = 5/√26

So,

Cos2X = 1- 2Sin²X

= 1- 2× (5/√26)²

= 1- 25/13

= (13-25)/13

= -12/13

✨Thats Answer✨

Answer 2

(refer the above pic for the diagram)

$\tan(x) = 5 = \frac{5}{1} = \frac{perpendicular}{base}$

$\sin(x) = \frac{5}{ \sqrt{26} } = > {sin}^{2}(x) = \frac{25}{26} \\ \cos(x) = \frac{1}{ \sqrt{26} } = > {cos}^{2}(x) = \frac{1}{26} \\ \\ \cos(2x) \\ = { \cos }^{2} (x) - {sin}^{2} (x) \\ = \frac{1}{26} - \frac{25}{26} \\ = \frac{ - 24}{26} \\ = \frac{ - 12}{13}$

Hence,

cos2x = -12/13.