Question

3. (1) Find the value of sin 2x,cos 2x and tan 2x,when tan x = 24/7 and x lies in third quadrant​

Answer 1

Answer:

sin2x = 336/625,

cos2x= - 527/625

tan2x = -336/527

Step-by-step explanation:

tan x = 24/7

=> tan 2x = 2tanx/(1-tan²x)

= (2×24/7) / (1-24²/7²)

= (48/7)×(- 49/527)

= - 48×7/527

= - 336/527

=> perpendicular = 336

=> base = 527

=> hypotenus = √(336²+527²) = 625

since x lies in third quadrant

=> 180°<x<270°

=> 360°<2x<540° => 0°<2x<180°

=> 2x lies in 1st or 2nd quadrant.

but tan 2x has (-ve) value

=> 2x lies in 2nd quadrant only.

sin 2x= 336/625

cos 2x = - 527/625

hope this helps you