Question

Prove that sin34°/sin56°+ co34°/cos56°=sec34°×cosec34°.

Answer 1

Formula used -
Sin A
=Cos(90°- A)
sinA²+cosA² = 1

Answer 2

LHS

Sin34/Sin56 + Cos 34/Cos56

= Sin(90-56)/Sin56 + Cos(90-56)/Cos56

= Cos56/Sin56 + Sin56/Cos56

= { Cos ^(2) 56 + Sin ^(2) 56 } / { Sin56 × Cos56 }

= 1 / Sin56 × Cos56

= 1 / { Sin(90 - 34) × Cos(90 - 34) }

= 1 / Cos34 × Sin 34

= Sec34 × Cosec 34

= RHS

Hence Proved. Please mark it as the brainliest as i have spent a lot of effort in typing it.