Trig Help - Need Help Verifying This Identity

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The discussion focuses on verifying the trigonometric identity sin x + tan x / (1 + cos x) = tan x. Participants emphasize the importance of clear expression formatting, particularly the use of parentheses and the distinction between hyphens and minus signs. A suggestion is made to replace tan x with sin x/cos x to simplify the left side of the equation. The clarity of the original expression is questioned, with multiple interpretations possible. Proper algebraic manipulation is necessary to confirm the identity.
dec1ble
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im trying to verify this identity - sin x + tan x / 1 + cos x = tan x - i get lost very easily and need the steps - can anyone help me?
 
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It might help if you took a little more care in writing your expressions with suitable placement of parentheses and properly distinguishing between hyphens and minus signs.
 
Tide's point is that it is not clear if you mean (sin x+ tan x)/(1+ cos x) or
sin x+ (tan x/(1+ cos x), or (-sin x+ tan x)/(1+ cos x) or...

Probably you mean (sin x+ tan x)/(1+ cos x)= tan x.

Hint: replace tan x by sin x/cos x. Then do the algebra to simplify the left side.
(1+ cos x is important!)
 
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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