Simplifying Trigonometric Identities

[yaseen shah]

in above image what is value of tan[theta].
a)y/y+2x b)x/x+y c)y/y+x d)y/x

This is not Home work! this question belongs to entry test.Which I
can not solve so please do not give hints.

 

[D H]

This looks like homework.

What do you think? The primary purpose of this site is to help students do their homework. We do not do it for you. Please show some work.

 

[Gerenuk]

Hint:
What is tan(x+\pi/4)

 

[SonyAD]

Hint:
What is tan(x+\pi/4)

What sort of hint is that?

 

[Gerenuk]

What sort of hint is that?

This forum is not for lazy students who don't want to do their homework and we are not supposed to do it for them. So I gave a hint only. With that hint you can solve the problem without any thought about geometry. It's a 4 line mathematical rearrangement.

 

[HallsofIvy]

What sort of hint is that?

It's and excellent one! I will admit that for a moment I forgot that the smaller right triangle had both legs of length x.

 

[Unit]

Gerenek, from your hint, I found the answer using the formula for tan(α+β). Is this an acceptable way to go about it? It took me than four steps...

 

[SonyAD]

My solution was both general and intuitive. It helps in understanding how & why. The insight gained will be useful in the real world.

The proverbial fishing pole.

It's and excellent one! I will admit that for a moment I forgot that the smaller right triangle had both legs of length x.

The solution based on the little triangle being isosceles won't work if it isn't.

 

[Gerenuk]

My solution was both general and intuitive. It helps in understanding how & why. The insight gained will be useful in the real world.

There is nothing intuitive about the need for new sketches and a length derivation. Also you fail the exam by running out of time if you solve the tasks much more generally than needed.

 

[HallsofIvy]

My solution was both general and intuitive. It helps in understanding how & why. The insight gained will be useful in the real world.

The proverbial fishing pole.

What solution? Your entire contribution to this thread was "What sort of hint is that?"

The solution based on the little triangle being isosceles won't work if it isn't.

In this problem it is. Gerunuk gave a hint to solve this problem.

 

[SonyAD]

It got deleted in exchange for an infraction.

 

[eumyang]

This is not Home work! this question belongs to entry test.Which I can not solve so please do not give hints.

Hints are all you'll get here, I'm afraid. If this question is from an entrance exam, and a student doesn't know how to do problems like these, then he/she shouldn't belong to the program/school/course he/she is entering?

Gerenuk's hint is excellent. Do you know your trigonometric identities?

With that hint you can solve the problem without any thought about geometry. It's a 4 line mathematical rearrangement.

It took me 6 lines, not 4, but I tend to write more steps than probably what is necessary. 69