Question

Cos^-1( 3+5cosx / 5+3cosx)

Answer 1

$\bf {Step \: 1: }$ The power of cos is negative. Therefore, simplify the sum in simpler form.

$\huge { \cos( \frac{3 + 5 \cos(x) }{5 + 3 \cos(x) } ) ^{ - 1}}$

$\bf {Step \: 2: }$ After simplifying the sum, use the formula of sin (x) = $\large {\frac {1}{cos (x)}}$

$\huge { = \frac{1}{ \cos( \frac{3 + 5 \cos(x) }{5 + 3 \cos(x) } ) } }$

$\bf {Step \: 3: }$ After using formula you get your answer...

$\huge { = \sec( \frac{3 + 5 \cos(x) }{5 + 3 \cos(x) } )}$

hope you'll get it..