i need help with this, how to solve it and whats the answer(s), with algebra and trig relations
#Help trig,
formal mantle
echo charmBOT
i need help with this, how to solve it and whats the answer(s), with algebra and...
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formal mantle
this should be the answers, but i need to know the method of solving it
warm minnow
ok
sin(x + pi) = sinxcospi + cosxsinpi
-sinx
square that
the LHS becomes
$4\sin^{2}{x}\cos^{2}{x}$
normal helmBOT
No Lifer?
warm minnow
$(2\sin{x}\cos{x})^2$
normal helmBOT
No Lifer?
normal helmBOT
No Lifer?
warm minnow
lets put this in the original equation
$\sin^{2}{(2x)} = \cos^{2}{(5x - \frac{\pi}{6})}$
normal helmBOT
No Lifer?
warm minnow
$\sin{(2x)} = \cos{(5x - \frac{\pi}{6})}$
normal helmBOT
No Lifer?
warm minnow
SO
2x and 5x-pi/6 are of the form (4n+1)pi/4 where n is an integer
lets take the mod to simplify things
$2x \equiv \frac{\pi}{4}$
$5x-\frac{\pi}{6} \equiv \frac{\pi}{4}$
$x \equiv \frac{\pi}{18}$
warm minnow
**No Lifer?**
now as we took mod pi:
$x = \frac{(18n+1)\pi}{18}$
hmmm
alr i'll just do it the normal way...
same answer...
normal helmBOT
No Lifer?
warm minnow
$x = k\pi + \frac{\pi}{18}, k \in Z$
normal helmBOT
No Lifer?
warm minnow
idk...
formal mantle
thank you very much, i didnt realize even to use the addition rule directly in the beginning, this makes sence, thank you :)
i was taking the root of both sides in the beginning , this made it easier