Question

Find the value of tan x, if cos x + 5 sin x  cos x = 3.​

Answer 1

Step-by-step explanation:

cos^2x+5sinxcosx=3

Dividing both sides by cos^2x then we get,

1+5tanx=3sec^x

3(1+tan^2x)-5tanx-1=0

3tan^2x-5tanx+2=0

3tan^2x-3tanx-2tanx+2=0

3tanx(tanx-1)-2(tanx-1)=0

(3tanx-2)(tanx-1)=0

so tanx=2/3

and tanx =1