prove that ( sin theta - cosec theta ) ( cos theta - sec theta) = 1/ tan theta + - Maths - Introduction to Trigonometry

Question

prove that ( sin theta - cosec theta ) ( cos theta - sec theta) =
1/ tan theta + cot theta

Priyanka Kedia · Accepted Answer

L H S
=sinθ-cosecθcosθ-secθ=sinθ-1sinθcosθ-1cosθ=sin2θ-1sinθcos2θ-1cosθ=-cos2θsinθ-sin2θcosθ=sinθcosθR
H S
=1tanθ+cotθ=1sinθcosθ+cosθsinθ=sinθ cosθsin2θ+cos2θ=sinθcosθ⇒L
H S =R H S Hence Proved

prove that ( sin theta - cosec theta ) ( cos theta - sec theta) = 1/ tan theta + cot theta .