Question

solve the question please

Answer 1

Answer:

$Question: \dfrac{Sin 34 }{ Sin 56 } + \dfrac{ Cos 34}{Cos 56} = Sec \:34 . Cosec \:34$

Sin A = Cos ( 90 - A )

Cos A = Sin ( 90 - A )

Now solving the sum,

Sin 56 = Cos ( 90 - 56 )

=> Sin 56 = Cos ( 34 )

Similarly,

Cos 56 = Sin ( 90 - 56 )

=> Cos 56 = Sin 34

Substituting the values in the question we get,

$\implies \dfrac{ Sin 34 }{ Cos 34 } + \dfrac{ Cos 34 }{Sin 34 } = Sec \: 34 + Cosec \: 34$

Considering the RHS, we get,

Taking LCM we get,

$\implies \dfrac{ Sin^2 \: 34 + Cos^2 \: 34 }{ Sin\:34.Cos \:34 }$

We know that, Sin A + Cos A = 1. Hence we get,

$\implies \dfrac{1}{ Sin\:34.\:Cos\:34} = \dfrac{1}{Sin\:34} . \dfrac{1}{Cos \:34} = Cosec\:34.\:Sec\:34$

Hence LHS = RHS

Hence Proved !