MHB Don't think there is a solution

  • Thread starter Thread starter dayalji
  • Start date Start date
AI Thread Summary
The discussion revolves around solving the equation involving cosecant and secant functions. A user initially presents a problematic equation with mismatched parentheses, leading to confusion. After clarifying the equation, it is determined that the left-hand side simplifies to zero, not fifty, indicating a typo. The correct manipulation of the equation ultimately shows that sec^2(x) equals 25. The importance of presenting progress in problem-solving is emphasized to facilitate better assistance.
dayalji
Messages
2
Reaction score
0
Hi if
cosec(x)/(1-cosec(x) -cosec(x)/(1-cosec(x)=50

show that sec^2(x)=25
 
Mathematics news on Phys.org
dayalji said:
cosec(x)/(1-cosec(x) -cosec(x)/(1-cosec(x)=50

Hi dayalji and welcome to MHB! :D

You have a mismatched parenthesis, so it's difficult to tell what the problem is. Please correct your work.

Also, we ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
greg1313 said:
Hi dayalji and welcome to MHB! :D

You have a mismatched parenthesis, so it's difficult to tell what the problem is. Please correct your work.

Also, we ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
Hi Greg1313
I have written question again. Problem is the expressions cancel each other out and keep ending with zero.

If $\frac{cosec(x)}{(1-cosec(x)} - \frac{cosec(x)}{(1-cosec(x)} =50 $

show that $sec^2(x)=25$
 
The left hand side of the equation you give above is identically 0, not 50.
 
I think I've found the typo . . .

\text{If }\dfrac{\csc}{1+\csc x} - \frac{\csc x}{1-\csc x} \:=\:50

\text{show that } \sec^2(x)\,=\,25
\begin{array}{cccc}<br /> \text{We have:} &amp; \dfrac{csc x}{1+\csc x} - \dfrac{csc x}{1 - \csc x} &amp;=&amp;50\\ \\<br /> &amp; \dfrac{\csc x(1-\csc x) - \csc x)1+\csc x)}{(1+\csc x)(1 - \csc x)} &amp;=&amp; 50\\ \\<br /> <br /> &amp; \dfrac{-2\csc^2x}{1-\csc^2x} &amp;=&amp; 50\\ \\<br /> <br /> &amp; \dfrac{\frac{-2}{\sin^2x}}{1 - \frac{1}{\sin^2x}} &amp;=&amp; 50 \\ \\<br /> <br /> &amp; \dfrac{-2}{\sin^2x-1} &amp;=&amp; 50\\ \\<br /> <br /> &amp; \dfrac{-2}{-\cos^2x} &amp;-&amp; 50 \\ \\<br /> &amp;2\sec^2x &amp;=&amp; 50 \\ \\<br /> &amp; \sec^2x &amp;=&amp; 25<br /> \end{array}

.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Just chatting with my son about Maths and he casually mentioned that 0 would be the midpoint of the number line from -inf to +inf. I wondered whether it wouldn’t be more accurate to say there is no single midpoint. Couldn’t you make an argument that any real number is exactly halfway between -inf and +inf?
Back
Top