Question

If cosec theta = u and cos theta = v, then cot theta is e we equal to?
a) u/v
b) v/u
c) u²v
d) uv
what is the correct answer. ​

Answer 1

Step-by-step explanation:

Correct option is

A

True

Given,

cosecθ+cotθ=k

sinθ1+sinθcosθ=k

sinθ1+cosθ=k

1+cosθ=ksinθ

Squaring both side,

(1+cosθ)2=k2sin2θ

(1+cosθ)2=k2(1−cos2θ)

(1+cosθ).(1+cosθ)=k2(1+cosθ)(1−cosθ)

1+cosθ=k2(1−cosθ)

1+cosθ=k2−k2cosθ

1+(1+k2)cosθ=k2

(1+k2)cosθ=k2−1

cosθ=k2+1k2−1

Answer 2

Answer:

d) uv

Step-by-step explanation:

Given that cosec theta = u and cos theta = v, we need to find cos theta.

Now,

cosecØ = u = 1/sinØ

cosØ = v = 1/secØ

Similarly,

cotØ = cosØ/sinØ

As 1/sinØ = u

So, sinØ = 1/u

Now,

Simply substitute the known values above,

→ cotØ = v/(1/u)

→ cotØ = uv

Hence, cotØ = uv.