Question

1+tana/sina+1+cota/cosa=2(seca+coseca)

Answer 1

hope this help.i have solved L.H.S .u can try from RHS too

Answer 2

The given trigonometric problem can probably use the identities :-

Sin a = tan a * cos a
1/cos a = sec a
1/sin a = cosec a

Now,

$\frac{1 + \tan(a) }{ \sin(a) } + \frac{1 + \cot(a) }{ \cos(a) } \\ \\ = \frac{1}{ \sin(a) } + \frac{ \sin(a) }{ \cos(a) \times \sin(a) } + \\ \frac{1}{ \cos(a) } + \frac{ \cos(a) }{ \sin(a) \times \cos(a) } \\ \\ = \csc(a) + \sec(a) + \sec(a) + \csc(a) \\ \\ = 2 \sec(a) + 2 \csc(a) \\ \\ = 2( \sec(a) + \csc( a) )$
Hence

Lhs = Rhs

Hence,
Proved