If y=1+sin θ+cos θ1+sin θ-cos θ, show that, dydθ+11-cos θ=0 - Maths - Relations and Functions

Question

If y = 1 + sin   θ + cos   θ 1 + sin  
θ - cos   θ ,   show   that ,   d y d
θ + 1 1 - cos   θ = 0

Lovina Kansal · Accepted Answer

Dear student

We have,y=1+sinθ+cosθ1+sinθ-cosθDifferentiate ot w
r t θ
, we getdydθ=cosθ-sinθ1+sinθ-cosθ-1+sinθ+cosθcosθ+sinθ1+sinθ-cosθ2⇒dydθ=cosθ+cosθsinθ-cos2θ-sinθ-sin2θ+sinθcosθ-cosθ-sinθ-sinθcosθ-sin2θ-cos2θ-sinθcosθ1+sin2θ+cos2θ+2sinθ-2sinθcosθ-2cosθ⇒dydθ=-2sinθ-22+2(sinθ-cosθ)-2sinθcosθ⇒dydθ=-21+sinθ21+sinθ-cosθ-sinθcosθ⇒dydθ=-1+sinθ11+sinθ-cosθ1+sinθ⇒dydθ=-1+sinθ1+sinθ1-cosθ⇒dydθ+11-cosθ=0
Regards

If y = 1 + sin θ + cos θ 1 + sin θ - cos θ , show that , d y d θ + 1 1 - cos θ = 0 .

If $y = \frac{1 + \sin θ + \cos θ}{1 + \sin θ - \cos θ}, show that, \frac{d y}{d θ} + \frac{1}{1 - \cos θ} = 0$ .