If 8sintheta=4+costheta, what is the value of tantheta ?

1 Answer
Jul 14, 2018

rarrtanx= 3/4

Explanation:

Let theta=x then

rarr8sinx=4+cosx

rarr(8sinx)/cosx=(4+cosx)/cosx=4/cosx+1

rarr8tanx=4secx+1

rarr8tanx-1=4secx

Squaring both sides, we get,

rarr64tan^2x-16tanx+1=16sec^2x=16(1+tan^2x)

rarr64tan^2x-16tanx+1=16+16tan^2x

rarr48tan^2x-16tanx-15=0

rarr48tan^2x+20tanx-36tanx-15=0

rarr4tanx(12tanx+5)-3(12tanx+5)=0

rarr(12tanx+5)(4tanx-3)=0

rarrtanx=-5/12 or 3/4

But x=tan^(-1)(-5/12) does not satisfy the equation so tanx=3/4