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Aug
2
answered Help needed in verifying a trigonometric identity
Aug
2
comment What are some good questions for this trick, if $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\dots=\alpha$ then $\alpha=\frac{a+c+e+…}{b+d+f+…}$?
Let us continue this discussion in chat.
Aug
2
revised What are some good questions for this trick, if $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\dots=\alpha$ then $\alpha=\frac{a+c+e+…}{b+d+f+…}$?
added 151 characters in body
Aug
2
comment What are some good questions for this trick, if $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\dots=\alpha$ then $\alpha=\frac{a+c+e+…}{b+d+f+…}$?
@125a8owp, archive.org/details/higheralgebraseq00hall and also archive.org/details/higheralgebra032813mbp
Aug
2
comment What are some good questions for this trick, if $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\dots=\alpha$ then $\alpha=\frac{a+c+e+…}{b+d+f+…}$?
@125a8owp, I used apply it in Trigonometry, too like : If $\displaystyle\tan x=\frac ab,\frac{\sin x}a=\frac{\cos x}b$ $\implies\frac{\sin^2x}{a^2}=\frac{\cos^2x}{b^2}=\frac{\sin^2x+\cos^2x}{a^2+b^2}‌​\implies \cos^2x=\cdots$ etc.
Aug
2
comment What are some good questions for this trick, if $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\dots=\alpha$ then $\alpha=\frac{a+c+e+…}{b+d+f+…}$?
@125a8owp, Two more. Try the last one
Aug
2
revised What are some good questions for this trick, if $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\dots=\alpha$ then $\alpha=\frac{a+c+e+…}{b+d+f+…}$?
added 115 characters in body
Aug
2
revised What are some good questions for this trick, if $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\dots=\alpha$ then $\alpha=\frac{a+c+e+…}{b+d+f+…}$?
added 115 characters in body
Aug
2
comment What are some good questions for this trick, if $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\dots=\alpha$ then $\alpha=\frac{a+c+e+…}{b+d+f+…}$?
@125a8owp, Edited
Aug
2
answered What are some good questions for this trick, if $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\dots=\alpha$ then $\alpha=\frac{a+c+e+…}{b+d+f+…}$?
Aug
2
comment Find all whole numbers such that the number increased by the sum of its digits equals 73.
$$11a+2b=73\iff11(a-5)=2(9-b)\iff\frac{a-5}2=\frac{9-b}{11}=c$$ $$\implies 0\le a=2c+5<10\iff c=0,1,2$$ and $$0\le9-11c=b<10\implies c=0$$
Aug
2
comment Evaluate $\int\frac {\csc^2{x}-2005}{\cos^{2005}{x}} dx $
@Samurai, $$\int\left(\frac{d(\sec^{2005}x)}{dx}\int\csc^2x\ dx\right)dx=\int2005\sec^{2004}x(\sec x\tan x)(-\cot x)\ dx=-2005\int\sec^{2005}x\ dx,$$ right?
Aug
1
comment A Trigonometric Question
@ThomasAndrews, If $\displaystyle\cos x=\cos y,-\cos^4\theta=\cos^2x\iff \cos\theta=\cos x=0$ for real $x,\theta$ . From the first line of Question, can't we safely assume $\cos\theta\cdot\sin\theta\ne0$?
Aug
1
comment Show that $ \frac{\tan x}{1+\sec x}+\frac{1+\sec x}{\tan x}= 2 \csc x$
@JohnJoy, Please find the edited version
Aug
1
revised Show that $ \frac{\tan x}{1+\sec x}+\frac{1+\sec x}{\tan x}= 2 \csc x$
deleted 20 characters in body
Aug
1
answered Evaluate $\int\frac {\csc^2{x}-2005}{\cos^{2005}{x}} dx $
Aug
1
comment A Trigonometric Question
@user161425, How about this? See also:math.stackexchange.com/questions/805602/…
Aug
1
answered How can I find $\lim_{x \to 0}\frac{\tan(3x)}{\sin(8x)}$ without L'Hospital's Rule
Aug
1
answered A Trigonometric Question
Aug
1
answered Evaluating limit $\lim_{x\to0_+} \frac{\sqrt{2x(1-x)} \log(1-x^2)}{(1-\cos x)\sqrt{\sin x}}$