prove that Cosec theta + cot theta = 1/cosec theta – cot theta

2 thoughts on “prove that Cosec theta + cot theta = 1/cosec theta – cot theta”

1. Answer:

   LHS=

   cotA+cosA

   cotA−cosA

   =

   sinA

   cosA

   +cosA

   sinA

   cosA

   −cosA

   =

   cosA

   cosA

   ×

   cosecA+1

   cosecA−1

   =

   cosecA+1

   cosecA−1

   =RHS

   Reply

2. Answer:

   Answer

   cosecθ+cotθ=

   cosecθ−cotθ

   1

   solving LHS.

   cosecθ+cotθ = (on rationalizing)

   (cosecθ−cotθ)

   (cosecθ+cotθ)(cosecθ−cotθ)

   cosecθ−cotθ

   cosec

   2

   θ−cot

   2

   θ

   =

   sin

   2

   θ

   1

   −

   sin

   2

   θ

   cos

   2

   θ

   [∵cosecθ=

   sinθ

   1

   cotθ=

   sinθ

   cosecθ

   ]

   cosecθ−cotθ

   sin

   2

   θ

   1−cos

   2

   θ

   =

   cosecθ−cotθ

   1

   [∵1−cos

   2

   θ=sin

   2

   θ]

   $$\because L.H.S =\frac{1}{cosec\theta-cot\theta} = RHS.

   Step-by-step explanation:

   answer verified by topper

   Reply