Question

tan a +sin a /tan a -sin b =sec a +1/seca -1
Prove that lhs = rhs

Answer 1

$\frac{tan \: a \: + sin \: a}{tan \: a \: - sin \: a} \\ \\ = \frac{ \frac{sin \: a}{cos \: a} + sin \: a}{ \frac{sin \: a}{cos \: a} - sin \: a} \\ \\ = \frac{sin \: a( \frac{1}{cos \:a } + 1) }{sin \: a( \frac{1}{cos \: a} - 1) } \\ \\ = \frac{ \frac{1}{cos \: a} + 1 }{ \frac{1}{cos \: a} - 1 } \\ \\= \frac{sec \: a + 1}{sec \: a - 1}$

= RHS

Answer 2

tana+sina

=

cosa

sina

−sina

cosa

sina

+sina

=

sina(

cosa

1

−1)

sina(

cosa

1

+1)

=

cosa

1

−1

cosa

1

+1

=

seca−1

seca+1

= RHS