Question

Cosec A (1+cos A) (cosec A-cot A)=1

Answer 1

Answer:

LHS = cosecA (1-cos A) (cosec A + cot A)

= (cosecA-cosecAcosA)(cosecA+cotA)

= (cosecA-cotA)(cosecA+cotA)

[ Since , cosecAcosA = cosA/sinA = cotA ]

= cosec²A - cot²A

= 1

[ Since , cosec²A - cot²A = 1 ]

= RHS

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Answer 2

let us take cosec A - cot A and simplify first

cosec A - cot A

⇒ 1/sina - cosa/sina

⇒1-cosa/sina

let us simplify Cosec A (1+cos A)

1/sina ( 1 + cosa)

1/sina + cosa/sina

1+cosa/sina

let us put all values in the equation

(1+cosa/sina)(1-cosa/sina)

1-cos²a/sin²a                                     (since (a+b)(a-b) = a²-b²)

sin²a/sin²a                                         (since 1-cos²a = sin²a)

1.

HENCE PROVED

HOPE THIS HELPS!!