Question

1 point
16. If tan-1 (cot O) = 20, then o
is equal to
O a) 11/3
O b) 1/4
O c) 1/6
O d) None of these​

Answer 1

Answer:

Given : cosec x - cot x =

3

1

.......... (1)

We know, cosec

2

x−cot

2

x=1

⟹ (cosec x - cot x)(cosec x + cot x) =1

⟹

3

1

(cosec x + cot x) =1

⟹ cosec x + cot x =3 ............ (2)

Solving (1) and (2) we get,

cosec x =

6

10

=

3

5

and cot x =

3

4

∴ sinx=

5

3

cosec x

cot x

=

5

4

∴ cosx=

5

4

∴ cos

2

x−sin

2

x=(

25

16

)−(

25

9

)=

25

7

Hence, option D is correct.

Step-by-step explanation:

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