Question

prove that
(1+cot2A) sin2A=1

Answer 1

(1+cot2A)sin2A=1

(1+cos2A/sin2A)sin2A=1

((sin2A+cos2A)/sin2A)sin2A=1

sin2A+cos2A=1 ....(1)

sin2A=1-cos2A

subsituiting the value of sin 2A in eq. (1)

1-cos2A+cos2A=1

1=1

hence proved.

Answer 2

Answer:

Identity : cosec

2

A−cot

2

A=1

LHS =(1+cot

2

A)sin

2

A

=cosec

2

A×sin

2

A

=

sin

2

A

1

×sin

2

A

=1

=RHS

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