Question

If 7cosec= 8, then cot theta/sin theta​

Answer 1

Answer:

Given that:

7cosecθ=8 or cosecθ=8/7

To find:

cotθ/sinθ=?

Formulae to be used:

1)cosecθ=1/sinθ or sinθ=1/cosecθ

2)sin²θ+cos²θ=1

3)cotθ=cosθ/sinθ

Solution:

As we know that, sinθ=1/cosecθ

∴sinθ=1/(8/7)

∴sinθ=7/8

now,

sin²θ+cos²θ=1

but sinθ=7/8

(7/8)²+cos²θ=1

(49/64)+cos²θ=1

cos²θ= 1-49/64

cos²θ= 15/64

cosθ=√15/8

and

cotθ=cosθ/sinθ

cotθ= (√15/8)/(7/8)

cotθ=√15/7

∴cotθ/sinθ=(√15/7)/(7/8)

=8√15/49