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I am Not Asking For Like 30° or 60°... I am Asking For Angles Like 36° , 22.5° ... etc Something Like These...

For Example :

tan 22.5° = √2 - 1
sin 18° = (√5 -1)/4

I am Not Asking For The Values, Just The Important AnglesValues I Can Take Out By Myself

Just Which Angles Do I Need To Remember

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2 Answers

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@Saikat Das, @peter petrov's opinion is indisputable. However, myself being an IIT aspirant, I can understand your concern. As you mentioned in the comment that there are $1.4\,\text{m}$ candidates appearing the exam but the toughest competitor you've to beat is time. In order to solve the questions in given time you have to be fast and agile which in turn requires memorization of few formulae and results.

The renowned author of mathematics for JEE, Dr.R.D. Sharma, in his book "Objective Mathematics Vol.II" has given trigonometric ratios of some important angles which are useful for IIT-JEE. Here are they: (I've mentioned only $\sin$ of the angles)

1. $\sin 15^\circ=\displaystyle\frac{\sqrt 3 -1}{2\sqrt 2}$

2. $\sin 22.5^\circ=\displaystyle\frac{1}{2}(\sqrt{2-\sqrt 2})$

3. $\sin 18^\circ =\displaystyle\frac{\sqrt 5-1}{4}$

4. $\sin 36^\circ=\displaystyle\frac{\sqrt{10+2\sqrt 5}}{4}$

5. $\sin 9^\circ=\displaystyle\frac{\sqrt{3+\sqrt 5}-\sqrt{5-\sqrt 5}}{4}$

6. $\sin 37^\circ\approx \displaystyle\frac{3}{5}$

7. $\cos 36^\circ-\cos 72^\circ=\displaystyle\frac{1}{2}$

8. $\cos 36^\circ\cos 72^\circ=\displaystyle\frac{1}{4}$

NOTE: This results are written just for completeness sake. If you check out past year papers they mostly ask trig ratios of standard angles and $37^\circ$. In your question you said that you can find the values by yourself. I suggest don't try except for $15^\circ$ and $22.5^\circ$ (as they are half of standard angles) because it is time consuming.

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I've never tried to remember the values of the trigonometric
functions for any angles other than $30°, 60°, 45°, 135°$.

I would be surprised if any math exam really requires memorizing
any such values just because math is not really about that.

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