Question

prove that: (sin ∅+ sec ∅)^2 + (cos ∅+ cosec ∅)^2 = (1 + sec ∅cosec ∅)^2​

Answer 1

$\underline{\underline{\maltese\: \: \textbf{\textsf{Answer}}}}$

(sin A + sec A)² + (Cos A + Cosec A)² !! (Sin A + 1/cos A)2 + (COS A + 1/ SinA)²

(Sin A Cos A + 1) / Cos A + (SinA COSA + 1)2 / Sin² A

= [ Sin A Cos A + 1][ 1/Cos? A + 1/Sin² A]

= [ Sin A Cos A + 1² [ Cos² A + Sin? A]/ [Sin A Cos² A]

= [ Sin A Cos A + 1] / [Sin²?A Cos²? A]

= [ (Sin A Cos A + 1) / (Sin A Cos A )]²

= (1 + 1/Sin A 1/Cos A)²

=(1 + Sec A Cosec A)²