If $cosec(\theta) + cot(\theta) = 6$, then:

$$a) \quad cosec(\theta) = \frac{35}{12}, \quad \cot(\theta) = \frac{37}{12}$$
$$b) \quad cosec(\theta) = \frac{37}{12}, \quad \cot(\theta) = \frac{35}{12}$$
$$c) \quad cosec(\theta) = \frac{41}{12}, \quad \cot(\theta) = \frac{31}{12}$$
$$d) \quad None \; of \: these.. $$

Question

If $cosec(\theta) + cot(\theta) = 6$, then:

$$a) \quad cosec(\theta) = \frac{35}{12}, \quad \cot(\theta) = \frac{37}{12}$$
$$b) \quad cosec(\theta) = \frac{37}{12}, \quad \cot(\theta) = \frac{35}{12}$$
$$c) \quad cosec(\theta) = \frac{41}{12}, \quad \cot(\theta) = \frac{31}{12}$$
$$d) \quad None \; of \: these.. $$

anonymous · Answer

would this be productive?
$$\frac{ 1 }{ \sin \theta }+\frac{ \cos \theta }{ \sin \theta }=6$$
$$1+\cos \theta=6\sin \theta$$
probably not.

anonymous · Answer

but this does
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anonymous · Answer

How you made that triangle and how you calculated those values?

anonymous · Answer

pythagorean theorem with the multiple choice answers given

anonymous · Answer

@campbell_st can you solve this by not using answer choices?

anonymous · Answer

Yes we can use the answer choices but what if the question says that you are given with cosecx + cotx = 6
find cosecx and cot(x),
then how will you find it??

anonymous · Answer

try to find x? I don't know.

anonymous · Answer

you can probably use a graphing calculator to find x.
graph y=6 sin theta - cos theta -1

anonymous · Answer

and find where y=0

anonymous · Answer

You are going deeper, I will not prefer this way, never mind..

Is their any simple way?? @hartnn @dumbcow @Luis_Rivera

anonymous · Answer

that or I would graph cosec x + cot x -6 and find y=0 for x
that's probably simpler

anonymous · Answer

that's the simple way
graph y=cosec x + cot x -6
find x with a graphing calculator
calculate values of cosec and cot for that x
you will get approximate values, but I don't know how to do anything better than that.

anonymous · Answer

It is just an aptitude type question, you have only 20 seconds to do it..

Can you do it in 20 seconds??

Ha ha h ha..

anonymous · Answer

only the multiple choice way

anonymous · Answer

I got the triangle in 20 sec

anonymous · Answer

Then yes I will prefer that way..

anonymous · Answer

Thank you very much @Peter14 ..

anonymous · Answer

once I knew to try that way
you're welcome.

raden · Answer

1+cosθ=6sinθ
square both sides
1+2cosθ+cos^2θ=36sin^2θ
1+2cosθ+cos^2θ=36(1-cos^2θ)
37cos^2θ+2cosθ-35=0
factor out!
(37cosθ - 35)(cosθ + 1) = 0
solve for cosθ, first

hartnn · Answer

^