Prove that :$\tan 70 - \tan 20 = 2\tan 40 + 4\tan 10$ My Attempt,  $$70-20=40+10$$ $$\tan (70-20)=\tan (40+10)$$ $$\dfrac {\tan 70 - \tan 20}{1+\tan 70. \tan 20 }=\dfrac  {\tan 40 + \tan 10 }{1-\tan 40. \tan 10 }$$   How should I move on?  Please help   Thanks
I am currently studying in class 10 and I am unable to do this problem. $$\tan 70 ° -\tan 20° -2 \tan 40° =4\tan 10°$$ Can anybody please help me.  Thanks!
I'm trying to write a page that calls PHP that's stored in a MySQL database. The page that is stored in the MySQL database contains PHP (and HTML) code which I want to run on page load.  How could I go about doing this? How do you become a vampire/werewolf in Elder Scrolls Online The game is released for a few days now. I have heard that you can turn into thoses beasts. I have a few questions about that   How do you turn into werewolf/vampire ? On the chat people said they can bite others but who bite them first? How long does the effect last ? Are there any cons ? Maybe if your are a vampire you take damage from the sun like in older Elder Scrolls ? I'm trying to show the following:  Let $f:X\to Y$ be a proper holomorphic map between connected, non-empty Riemann Surfaces. Show that a map $g:Y\to\mathbb{C}$ is  holomorphic if and only if  its composition with f is holomorphic.  So far I know that $f$ is surjective, since it's proper and holomorphic. My next step was to look at the charts, but it's there, I get stuck. What does the 'grep' command do? I would like to learn how to use it so I can start to use the terminal more. Fonts larger than \Huge? How can I make text that is larger than the size of the output of {\Huge ...}?   I would like to be able to make text arbitrarily large (even if that is done by some suboptimal scaling routine). C++ virtual function from constructor How can see call history in iPhone one month back, i also tried with tried party software but that is not perfect , is the any solution from apple? I'm trying to make a basic Windows application that builds a string out of user input and then adds it to the clipboard. How do I copy a string to the clipboard using Python? How to make a standalone document with one equation? Right click not working on Ubuntu 18.04 I have installed Ubuntu 18.04 LTS on my HP Pavilion series laptop. After installing this version of Ubuntu, right click is not working of my touchpad. How can I solve this?  BTW:  does not have any solution which which is working for me. PS:- Problem remains after selection area in gnome-tweak-tool Replace non-numeric with empty string Quick add on requirement in our project.  A field in our DB to hold a phone number is set to only allow 10 characters.  So, if I get passed "(913)-444-5555" or anything else, is there a quick way to run a string through some kind of special replace function that I can pass it a set of characters to allow?  Regex? When is the formula $$S_{\infty} = \dfrac{a}{1-r}$$ valid?   Does |$r| &lt;1$? Number of $(0,1)$ $m\times n$ matrices with no empty rows or columns Problem  Let $n \geq 3$ be an odd number and let $G=\{1,...,2n\}$ be a group of order $2n$. Let $\phi:G \to S_{2n}$ be the morphism defined by $\phi(g_i)(g_j)=g_ig_j$ and let $H=\phi^{-1}(A_{2n})$. Show that $H$ is a proper normal subgroup of $G$.  So basically the result of this problem is that every group of order $2n$, with $n$ odd, is not simple.   The morphism $\phi$ can be seen as the action of $G$ on itself by left multiplication. Since $A_{2n} \lhd S_{2n}$, then $H=\phi^{-1}(A_{2n}) \lhd G$. I am stuck at showing that $H \neq \{1\},G$. All I could think of is that $G$ has an element $g$ of order $2$, then $\phi(g)$ is of order $1$ or $2$, but it is easy to see that $\phi(g)=1$ if and only if $g=1$, so $ord(\phi(g))=2$. I don't know which are the elements of order two in $S_{2n}$. I would appreciate some help to solve the problem, thanks in advance. Why is $H(k\mathbin\Vert x)$ not a secure MAC construction? Does Java Connection.close rollback? It is easy to find the minimum of $\|Ax-b\|_2$, when $A$ has full column rank. But how is the case when we add the constraint $\|x\|_2=1$? Or, to be explicit,  $$\min_{\|x\|_2=1}\|Ax-b\|_2=?$$  My idea is to construct the corresponding Lagrange function  $$L(x,\lambda) = (Ax-b)^T(Ax-b) + \lambda(x^T x - 1)$$  Differentiate the function with respect to $x,\lambda$, we have  $$A^T A x - A^T b + \lambda x = 0$$  $$x^T x=1$$  However, I find it hard to move forward to get the answer. Could anyone help me? Thanks a lot! What are Vertex and Pixel shaders? I'm trying to figure out the best way to model the sphere-spiral here:    Is it possible to make this shape directly? Or do you have to make it as a cylinder and wrap it to a sphere? "How big of a problem" vs. "how big a problem" Quite a few phrases in English are constructed like so:     How [adjective] a [noun]...?   This is the question form of the construction, which is often answered with the negative:     Not that [adjective] a [noun].   or the positive:     Quite [adjective] a [noun].   However, from time to time I'll hear the word 'of' inserted before the 'a', e.g.:     Not that [adjective] of a [noun].   This usually sounds wrong to me, with the exception of the case where the adjective 'much' is used.  So, this sounds fine to my ear:     Not that much of a problem.   whereas this doesn't:     Not that loud of a noise.   Why is it that 'much' should be used with 'of', and other adjectives not?  Is it because 'much' is seen as measuring a quantity (of something), whereas other adjectives that may be used in this construction are seen as measuring the quality of a whole thing?