# What should I study to know how to solve?

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I'm studying for a test, and they have several questions I've never dealt with, and I don't even know what the topics I should study are. Here are some of them:

#cos δ = 1# , which of the following could NOT be a value of #δ# ?

Which of the following is equivalent to #2sin2θ+(1–cos2θ)/(tan2θ)# ?

If #sin∂=sqrt32# , what is the value of #cot∂# ?

All that I want to know is WHAT I SHOULD STUDY to know how to solve these type of questions, since I have no idea how to even tackle them. I don't actually need the answers, just the names of the methods. Thanks!

I'm studying for a test, and they have several questions I've never dealt with, and I don't even know what the topics I should study are. Here are some of them:

Which of the following is equivalent to

If

All that I want to know is WHAT I SHOULD STUDY to know how to solve these type of questions, since I have no idea how to even tackle them. I don't actually need the answers, just the names of the methods. Thanks!

##### 1 Answer

For the first question, know your unit circle and special angles. Here is an image:

So if

For the second, you need to know your trig identities. Here is a picture of those that I think are most necessary to learn.

We can simplify as

#2(2sinthetacostheta) + (1 -(1 - 2sin^2theta))/((tan theta + tan theta)/(1 - tanthetatantheta)#

#4sinthetacostheta + ((2sin^2theta)(1 -tan^2theta))/(2tantheta)#

#4sinthetacostheta + (2sin^2theta - 2sin^2thetatan^2theta)/(2tantheta)#

#4sinthetacostheta+ sin thetacostheta- sin^2thetatantheta#

#5sinthetacostheta - sin^3theta/costheta#

A lot of expressions cancel to things like

As for the last problem, this example is implausible as

Now from above you can see that

#1 +cot^2alpha = 32#

#cot^2alpha = 31#

#cotalpha= +-sqrt(31)#

If they clarify that

Hopefully this helps, please ask if you have any further questions!