Question

Complete the following activity prove (1 + cot2θ) (1 – cosθ) (1 + cos θ) = 1​

Answer 1

L.H.S. = (1+cot

2

θ)(1−cosθ)(1+cosθ)

⇒ L.H.S. = (1+cot

2

θ)(1−cos

2

θ)

⇒ L.H.S. = cosec

2

θsin

2

θ

       

[∵1+cot

2

θ=cosec

2

θand1−cos

2

θ=sin

2

]

⇒ L.H.S. = cosec

2

θsin

2

θ

⇒ L.H.S. =  

sin

2

θ

1

​

×sin

2

θ=1=R.H.S.      [∵cosecθ

sinθ

1

​

∴cosec

2

θ

sinθ

1

​