Question

Sec theta -1/tan theta=tan theta/sec theta+1

I need the steps to get the other side of the equal sign, I have been trying with my group for a couple of days and can’t figure it out

Answer 1

in numerator, you have (sec x - 1) and in denominator, you have (sec x + 1) AND there is tan x too. Using the formula [sec^2 x - 1 = tan^2 x] might help.

$LHS \\ \\ = \frac{ \sec \: x - 1 }{ \tan \: x } \\ \\ = \frac{ \sec \: x - 1 }{ \tan \: x } \times \: \frac{ \sec \: x + 1 }{ \sec \: x + 1} \\ \\ = \frac{ \sec^2 \: x - 1 }{ \tan \: x( \sec \: x + 1) } \\ \\ = \frac{ \tan ^2 \: x }{ \tan \: x( \sec \: x + 1) } \\ \\ = \frac{ \tan \: x }{ \sec \: x + 1 } \\ \\ = RHS$