# If cosec tita+cot tita : k then prove that cos tita : k2-1/k2+1

2
by Runku
question is incomplete
Now it is complete .answer it

2014-10-01T14:53:09+05:30

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Cosec β + cot β = k
⇒1/sin β + cos β/sin β = k
⇒(1 + cos β) / sin β = k
⇒(1 + cos β) / √(1 - cos² β) = k
⇒(1 + cos β) / √(1 + cos β)(1 - cos β)= k
⇒√[(1 + cos β) / (1 - cos β)] = k
⇒(1 + cos β) / (1 - cos β) = k²/1
⇒[(1 + cos β) - (1 - cos β) ]/[(1 - cos β) + (1 + cos β) ] = (k²-1)/(k²+1)
(using the formula if
then )

⇒(2 cos β)/ 2 = (k²-1)/(k²+1)
⇒cos β = (k²-1)/(k²+1)
2014-10-01T17:01:13+05:30
Δ Given that ,
cosecα+cotα = K

or,

or,
Now squaring both side of this Eqn,
or,
or,

or,

or,

or,

or,

or,

therefore ,

or,

so,
Proved
And,         cosα+1 = 0
so, cosα = -1