How do you solve $3 sin x + 2 = tan 75$ $3sinx+2=tan75$ ?

Question

2012 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-09T02:27:14

$:.x=npi+(-1)^nalpha$
where $sin^-1(1/sqrt3)=alpha$

$3sinx+2=tan75=(tan30+tan45)/(1-tan30tan45)$

$=>3sinx+2=(1/sqrt3+1)/(1-1/sqrt3xx1)$

$=>3sinx+2=(sqrt3+1)/(sqrt3-1)$

$=>3sinx+2=(sqrt3+1)^2/((sqrt3-1)(sqrt3+1)$

$=>3sinx+2=(4+2sqrt3)/(3-1)$

$=>3sinx+2=2+sqrt3$

$=>3sinx=sqrt3$

$=>sinx=sqrt3/3=1/sqrt3==sinalpha$

where $sin^-1(1/sqrt3)=alpha$

$:.x=npi+(-1)^nalpha$

$"where "n=+-1,+-2,+-3....$

How do you solve 3sinx+2=tan753sinx+2=tan753sinx+2=tan75?