Question

can someone proof "tan(x).tan(x/2)=sec(x)-1​

Answer 1

Step-by-step explanation:

$\tan(x) \times \tan( \frac{x}{2} )$

=

$\frac{ \sin(x) }{ \csc(x) } \times \frac{1 - \csc(x) }{ \sin(x) }$

=

$\frac{1 - \csc(x) }{ \csc(x) }$

=

$\frac{1 - \frac{1}{ \sec(x) } }{ \frac{1}{ \sec(x) } }$

=

$\frac{ \frac{ \sec(x) - 1 }{ \sec(x) } }{ \frac{1}{ \sec(x) } }$

=

=

$\frac{ \sec(x) - 1}{1}$

=

$\sec(x) - 1$