Question

simplify (1+cotpower2 0)(1-cos0)(1+cos0)​

Answer 1

Answer:

Step-by-step explanation:

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

​

]