Question

(cot 6+3) (3 cot 0+1) = 3 cosec 0 +10 cot 6​

Answer 1

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Evaluate:

cot

−1

3

1

−cosec

−1

(−2)+sec

−1

(

3

2

)

Hard

Solution

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Given, cot

−1

3

1

−cosec

−1

(−2)+sec

−1

(

3

2

)

Let x=cot

−1

3

1

=

2

π

−tan

−1

3

1

We know that range of tan

−1

is (

2

−π

,

2

π

)

=

2

π

−

6

π

=

6

3π−π

=

6

2π

=

3

π

∴x=

3

π

Let y=cosec

−1

(−2)

since cosec

−1

x=sin

−1

x

1

⇒y=sin

−1

(

2

−1

)