Question

Please help with these

Answer 1

The values would be

sin2x = -3/5

cos2x = -4/5

tan2x = 3/4

What are double angles in trigonometry?

The double angle formulas are used to find the values of double angles of trigonometric functions using their single angle values. For example, the value of cos 30° can be used to find the value of cos 60°. Also, the double-angle formulas can be used to derive the triple-angle formulas.

Given: tanx = -3

Now as we know,

                  $sin2x=\frac{2tanx}{1+tan^2x}\\\\sin2x=\frac{2(-3)}{1+(-3)^2}\\\\sin2x=\frac{-6}{10}\\\\sin2x=\frac{-3}{5}$

Now

               $cos2x=\frac{1-tan^2x}{1+tan^2x}\\\\cos2x=\frac{1-(-3)^2}{1+(-3)^2}\\\\cos2x=\frac{1-9}{1+9}\\\\cos2x=\frac{-8}{10}\\\\cos2x=\frac{-4}{5}$

And similarly, we can find the value of tan2x, as

                  tan2x = sin2x/cos2x

                             = (-3/5)/(-4/5)

                             = 3/4

Hence,

The values would be

sin2x = -3/5

cos2x = -4/5

tan2x = 3/4

To learn more about double angles in trigonometry, visit:

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