Solve Trig Equation: 1+cos(180+2u) let 90+u be f

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To solve the equation 1 + cos(180 + 2u), the transformation using cos(180 + X) = -cos(X) simplifies it to 1 - cos(2u). This leads to the expression 1 - (2cos^2(u) - 1), which simplifies further to 2 - 2cos^2(u). The discussion highlights the importance of recognizing trigonometric identities to simplify equations effectively. Ultimately, the participants emphasize finding easier methods to approach trigonometric problems.
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Lol this one troubling me badly.

Simplify 1+cos(180+2u) let 90+u be f
1+cos(2f)
then 1+ cos^2 (f) - sin^2 (f)
umm then it's 2 Cos^2 (f)

lol I'm a bit lost.

what do you after that lol, or do you do it an easier way .Thanks in advance :cry:
 
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Easier way. Dont forget that cos(180+X) = -cos(X)
Therefrore cos(180+2u) = -cos(2u). Can u go from there?
 
Ah yea. lol thanks very much. I can.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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