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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)

⇒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)

cosecα+cotα = K

or,

or,

Now squaring both side of this Eqn,

or,

or,

or,

or,

or,

or,

or,

therefore ,

or,

so,

And, cosα+1 = 0

so, cosα = -1