I have my maths exam on Tuesday and cannot remember how to do trigonometric identities at all. I was so sure, but now I'm not. I asked a similar question earlier, but I still don't quite understand. Please give me step-by-step instructions?
[sinx + tanx] / [cosx +1] = tanx
I just got done with thi stuff and these are the formulas that helped me with alot.
tan(angle)=opposite/adjacent
coa(angle)=adjacent/hypotenuse
sin(angle)=opposite/hypotenuse
Is this what your asking for?
that's sort of a tricky one,
[sinx + tanx] / [cosx +1] = tanx
LS = (sinx + tanx)/(cosx+1) [(cosx-1)/cosx-1)]
= (sinxcosx - sinx + sinx - sinx/cosx)/(cos^2x - 1)
= [ (sinxcos^2x - sinx)/cosx]/(cos^2x - 1)
= sinx[cos^2x - 1)/cosx] / (cos^2x - 1)
= sinx/cosx
= tanx
= RS
Sure! I'd be happy to help you understand how to prove the trigonometric identity:
[sinx + tanx] / [cosx + 1] = tanx.
To prove this identity, we'll start with the left-hand side (LHS) of the equation and manipulate it algebraically until we end up with the right-hand side (RHS). Here's the step-by-step process:
Step 1: Simplify the LHS by expressing tanx in terms of sinx and cosx.
Since tanx = sinx / cosx, we can rewrite the numerator of LHS as sinx + sinx/cosx.
Step 2: Combine the terms in the numerator.
Using the common denominator cosx, we can combine the terms sinx and sinx/cosx to get (sinx * cosx + sinx) / cosx.
Step 3: Factor out sinx in the numerator.
Factor out sinx from the numerator: sinx * (cosx + 1) / cosx.
Step 4: Simplify the denominator.
Divide the numerator and denominator by cosx to simplify the expression: sinx * (cosx + 1) / cosx ÷ (cosx / cosx).
This becomes sinx * (cosx + 1) / 1, which simplifies to sinx * (cosx + 1).
Step 5: Compare the result with the RHS.
Now, we have sinx * (cosx + 1) on the LHS, and tanx on the RHS.
Recall that tanx = sinx / cosx. By multiplying the numerator and denominator of tanx by (cosx + 1), we get sinx * (cosx + 1) / cosx.
Step 6: Conclusion.
Since both sides of the equation simplify to the same expression, sinx * (cosx + 1), we have proven that the original trigonometric identity is true.
So, [sinx + tanx] / [cosx + 1] = sinx * (cosx + 1) = tanx.
Just keep practicing these steps, and you'll soon become comfortable with trigonometric identities. Good luck on your exam!