Question

prove that tan -1x+ cot -1=π/2,x€R​

Answer 1

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Answer 2

Answer:

Consider the L.H.S.

=tanx+cotx

=

cosx

sinx

+

sinx

cosx

=

sinx.cosx

sin

2

x+cos

2

x

We know that

sin

2

x+cos

2

x=1

Therefore,

=

sinx.cosx

1

=secx.cosecx

Hence, proved.

We have,

=sec

2

x+cosec

2

x

=

cos

2

x

1

+

sin

2

x

1

=

sin

2

x.cos

2

x

sin

2

x+cos

2

x

=

sin

2

x.cos

2

x

1

=sec

2

x.cosec

2

x

Hence, proved.