Question

If cos x = 4 sin x then cot x * 1 point 1/4 1/3 4 3

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