Question

If 6tan α + 2sec α = tan α + 5sec α, what is the value of sin α?​

Answer 1

$\sf \bf {\boxed {\mathbb {answer: }}}$

$If  \: 6tan(a)+2sec(a)=tan(a), + 5sec(a) \\ what \: is \: the \: value \: of \:  sin(a)? \\ \red {solution: } \\ \green{6tan(a)+2sec(a)=tan(a) + 5sec(a)} \\ \pink {∴6 \times \frac{sin \: (a)}{cos(a)} + \frac{2}{cos \: (a)} = \frac{sin \: (a)}{cos(a)} + \frac{5}{cos \: (a)} } \\ \orange{∴cos \: (a) \times (\frac{6sin \: (a)}{cos \: (a)} + \frac{2}{cos \: (a)} ) = cos \: (a)\times (\frac{sin \: (a)}{cos \: (a)} + \frac{5}{cos \: (a)}) } \\ \blue{∴cos \: (a) \times \frac{6sin \: (a)}{cos \: (a)} + cos \: (a)\times \frac{2}{cos \: (a)} = cos \: (a) \times \frac{sin \: (a)}{cos \: (a)} + cos \: (a) \times \frac{5}{cos \: (a)} } \\ \red{∴6sin(a)+2=sin(a)+5} \\ \blue {∴5sin(a)+2=5} \\ \pink{∴5sin(a)=3} \\∴ sin(a)= \frac{3}{5} \\ \orange{∴sin(a)=0.6435011} \\ \green{sin(a)=0.6}$