Question

Senx tgx/cscx-ctgx-senx=tgx

Answer 1

(senx + tanx) / (cotx + cscx) -------------------------- : cotx = 1/tan ; cscx = 1/senx 

= (senx + tanx) / [ (1/tanx) + (1/senx) ] 

= (senx + tanx) / [ ( (1 * senx) + (1 * tanx) ) / (tanx * senx) ] 

= (senx + tanx) / [ (senx + tanx) / (tanx * senx) ] 

= (senx + tanx) * [(tanx * senx) / (senx + tanx)] -------------- : a / (b/c) = a * (c/b) 

= (tanx * senx) * [(senx + tanx) / (senx + tanx)] ---------- : a * (c/b) = ac/b = ca/b = c * (a/b) 

= (tanx * senx) * 1 

= tanx * senx 

= senx * tanx