Prove the following:
sin theta /1- cos theta = cosec theta + cot theta
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Answer:
We have,
L.H.S. =
1−cosθ
sinθ
⇒ L.H.S. =
(1−cosθ)
sinθ
×
(1+cosθ)
(1+cosθ)
... [Multiplying numerator and denomenator by (1−cosθ)]
⇒ L.H.S. =
1−cos
2
θ
sinθ(1+cosθ)
[∵(1+cosθ)(1−cosθ)=1−cos
2
θ]
⇒ L.H.S. =
sin
2
θ
sinθ(1+cosθ)
[∵1−cos
2
θ=sin
2
θ]
⇒ L.H.S. =
sinθ
1+cosθ
⇒ L.H.S. =
sintheta
1
+
sinθ
cosθ
⇒ L.H.S. = cosecθ+cotθ=R.H.S.
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