Question

1+cos theta/1-cos theta=(cosec theta +cot theta) ²​

Answer 1

Answer:

Please refer the image,

Step-by-step explanation:

Answer 2

Answer:

1+cosθ/1-cosθ is equal to  (cosecθ + cotθ)

Step-by-step explanation:

Given that 1+cosθ/1-cosθ

We have to prove that 1+cosθ/1-cosθ = (cosecθ + cotθ)

Take L.H.S

Let θ = α

1+cosα/1-cosα = ( cosecα +cotα)

LHS = $\frac{1+cos\alpha }{1-cos\alpha }$ = $\frac{1+cos\alpha }{1-cos\alpha } *\frac{1+cos\alpha }{1+cos\alpha }$

            =$\frac{(1+cos\alpha )^{2} }{1^{2} -cos^{2}\alpha }$

sin²α +cos²α = 1

1 - cos²α = sin²α

$\frac{1+cos\alpha }{1-cos\alpha }$ =  $\frac{(1+cos\alpha )^{2} }{1^{2} -cos^{2}\alpha }$

          = $\frac{(1+cos\alpha )^{2} }{sin^2{\alpha } }$

        =  $(\frac{1+cos\alpha }{sin\alpha } )^{2}$

        = $(\frac{1}{sin\alpha } +\frac{cos\alpha }{sin\alpha } )^{2}$

        = (cosecα + cotα)² = RHS

∴LHS = RHS

Therefore,  1+cosθ/1-cosθ = (cosecθ + cotθ)

Hence proved.