Saved Bookmarks
| 1. |
Prove sin theta(1+tan theta)+cos theta(1+cot theta)=sec theta+cosec theta |
|
Answer» ANSWER:Sinθ(1 + Tanθ) + Cosθ(1 + Cotθ) = Secθ + Cosecθ Step-by-step explanation: Sin theta( 1+tan theta) + COS theta(1+ cot theta) = sec theta + cosec theta Sinθ(1 + Tanθ) + Cosθ(1 + Cotθ) = Secθ + Cosecθ LHS = Sinθ(1 + Tanθ) + Cosθ(1 + Cotθ) Using Tanθ = Sinθ/Cosθ & Cotθ = Cosθ/Sinθ = Sinθ(1 + Sinθ/Cosθ) + Cosθ(1 + Cosθ/Sinθ) = (Sinθ/Cosθ)(Cosθ + Sinθ) + (Cosθ/Sinθ)(Sinθ + Cosθ) = (Cosθ + Sinθ) (Sinθ/Cosθ + Cosθ/Sinθ) = (Cosθ + Sinθ)((Sin²θ + Cos²θ)/CosθSinθ) Using Sin²θ + Cos²θ = 1 = (Cosθ + Sinθ)/CosθSinθ = Cosθ/CosθSinθ + Sinθ/CosθSinθ = 1/Sinθ + 1/Cosθ = Cosecθ + Secθ = Secθ + Cosecθ = RHS QED Proved Sinθ(1 + Tanθ) + Cosθ(1 + Cotθ) = Secθ + Cosecθ Step-by-step explanation: |
|