Question

Find sin 2x, cos 2x, tan 2x if sec x = - 13/5, π/2 < x < π

Answer 1

sec x = - 13/5, π/2 < x < π

We know that

Sec² x = 1 + tan² x

tan²x = 169/25 -1 = 144/25

tan x = ± 12/5

Since π/2 < x < π

x lies in the 2nd quadrant. tan x < 0

∴ tan x = -12/5

   sin 2x = \(\frac{2 tan\,x}{1+tan^2x}\)