Question

1+cotA/cosa +1+tanA/sinA = 2(secA+cosecA)​

Answer 1

★ To Prove :-

• $\sf \dfrac{1 + \cot(A) }{ \cos(A) } + \dfrac{1 + \tan(A) }{ \sin(A) } = 2( \sec A + \csc \: A)$

★ Solution :-

$\sf \: LHS = \dfrac{1 + \cot(A) }{ \cos(A) } + \dfrac{1 + \tan(A) }{ \sin(A) }$

$\sf \implies \dfrac{ \sin(A) (1 + \dfrac{ \cos(A) }{ \sin(A) } ) + \cos(A) (1 + \dfrac{ \sin(A) }{ \cos(A) } )}{ \sin(A) \cos(A) }$

$\implies \sf \: \dfrac{ \sin(A) + \cos(A) + \cos(A) + \sin(A) }{\sin(A) \cos(A)}$

$\implies \sf \: \dfrac{2 \sin(A) }{\sin(A) \cos(A)} + \dfrac{2 \cos(A) }{\sin(A) \cos(A)}$

$\implies \sf \: 2( \dfrac{1}{ \cos(A) } + \dfrac{1}{ \sin(A) } )$

$\implies \sf \: 2( \sec(A) + \csc(A) ) = RHS$

Hence, Proved !

Answer 2

Answer:

see the attachment for the solution.