Oct 9, 2022 · Deriving the exact value of sin π/12 sin π / 12 using double angle identity Double angle identity - sin 2A = 2 sin A cos A sin 2 A = 2 sin A cos A So, sin(2 π12 ...

I am trying to evaluate: $$\int_0^ {\pi/12} \ln (\tan x)\,dx$$ I think the integral is quite simple but I am having a hard time evaluating it. I started with the result: $$\int_0^ {\pi/4} \ln (\tan x)...

Aug 24, 2019 · How to refactor $\pi / 12$ into $\pi /4 - \pi /3$ (standard calculus angles)? How do you know that $\pi / 12$ converts exactly into $\pi /4 - \pi /3$? Do I need to memorize that or is there a simple

Jun 21, 2016 · The equation/formula $$ \frac {\pi^2} {12} = \sum_ {n=1}^ {\infty} \frac { (-1)^ {n+1}} {n^2}$$ is to be derived. I know that the Fourier expansion of $f (x)=x$ for ...

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Feb 22, 2020 · Let −π/6 <θ <−π/12 − π / 6 <θ <− π / 12. Suppose α1 α 1 and β1 β 1 are the roots equation x2 − 2x sec θ + 1 x 2 − 2 x sec θ + 1..

Aug 10, 2020 · In the book Pi: A Source Book I found the following: Extract the square root of twelve times the diameter squared. This is the first term. Dividing the first term repeatedly by 3, obtain other ter...

May 9, 2023 · This question shows research effort; it is useful and clear

Given x ≥ y ≥ z ≥ π/12 x ≥ y ≥ z ≥ π / 12, x + y + z = π/2 x + y + z = π / 2, find the maximum and minimum of cos x sin y cos z cos x sin y cos z. I tried using turn sin y sin y to cos(x + z) cos (x + z), and Jensen Inequality, but filed. Please help. Thank you. *p.s. I'm seeking for a solution without calculus.

Aug 9, 2020 · Pretty self explanatory. If I had for example something like sin−1(π/12) sin − 1 (π / 12) in an expression, is it ever possible to express that expression without inverse trig functions?