Are $\cos^2 \theta$ and $\cos \theta^2$ the same? I mean be it $\sin,\cos, \tan ,\cot ,\sec,\csc$. Are they same? Please help a maths noob here.
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5$\cos^2\theta$ is the same thing as $(\cos\theta)^2$, it's just another notation. But these are different from $\cos(\theta^2)$. – Augustin Feb 24 '16 at 09:09
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2brackets are not mathematical jewellery only. They have a purpose.... – Bhaskar Vashishth Feb 24 '16 at 12:16
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No, they are not the same.
When you type $\cos^2 \theta$ you actually mean $(\cos \theta)^2$.
When you type $\cos \theta^2$ you mean $\cos(\theta ^2)$.
Onil90
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Thanks now i confusion was cleared,my text book directly skipped many steps so i could barely understand,I'm just a high school entrant – Trignometry Feb 24 '16 at 09:13
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@Trignometry Your textbook skipped many steps? I severly doubt that they skipped the step where the explained the notation $\cos^2(x)$. – gebruiker Feb 24 '16 at 09:15
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1Don't worry! It's normal to be confused at the beginning if the notation is not very clear. :) – Onil90 Feb 24 '16 at 09:16
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The first notation is used to mean $$\cos^2 \theta = \left( \cos \theta \right)^2$$ Your second notation will usually be read as $$\cos \theta^2 = \cos \left( \theta^2 \right)$$ although it is sometimes preferred to use the notation in the right-hand side to be clear.
They are not the same since $$\left( \cos \theta \right)^2 = \cos\theta\cos\theta \ne \cos(\theta\theta) = \cos(\theta^2)$$
StackTD
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Why was there a downvote for question,did i ask something wrong ?I did search but could find anything help ful. Let me know if i made some mistake so i could correct that in future – Trignometry Feb 24 '16 at 09:16
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@Trignometry I didn't give the downvote, but I presume the downvote was due to your poor formatting. Using MathJax is encouraged. – 5xum Feb 24 '16 at 09:17
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It wasn't my downvote, but I'll edit your question to the required formatting. – StackTD Feb 24 '16 at 09:20
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I'll learn mathjax before i post a new question in the future that's for the suggestion – Trignometry Feb 24 '16 at 09:23
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It's a matter of syntax.
In handwriting or literature: $\sin^{2} x \equiv (\sin x)^{2}$ and $\cos x^{2} \equiv \cos (x^{2})$;
however for computer software, say Mathematica:
Cos[x]$^2$ refers to $(\cos x)^2$ while Cos[x$^2$] refers to $\cos (x^{2})$.
Should be very careful.
Ng Chung Tak
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