Question

If sinX +cosX =1/5 then tan2X equals to ?​

Answer 1

Answer:

24/7

Step-by-step explanation:

Given,

sin x + cos x = 1/5

Squaring on both sides,

sin2x + cos2x + 2 sin x cos x = 1/25

1 + sin 2x = 1/25

sin 2x = (1/25) – 1

sin 2x = -24/25

Using the identity sin2A + cos2A = 1,

cos 2x = √[1 – (576/625)] = √(49/625) = 7/25 or -7/25

When cos 2x = 7/25,

tan 2x = sin 2x/cos 2x = (-24/25)/ (7/25) = -24/7

When cos 2x = -7/25,

tan 2x = 24/7