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

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Answer 1 · 2018-07-14T08:43:27

$rarrtanx= 3/4$

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 $tanx=3/4$

If 8sintheta=4+costheta8sintheta=4+costheta, what is the value of tanthetatantheta ?