Question

plzz help me with this trig proof ​

Answer 1

Answer:

Step-by-step explanation:

$\frac{sin3A}{cosA} + \frac{cos3A}{sinA}$

$\frac{sin3AsinA}{sinAcosA} + \frac{cos3AcosA}{sinAcosA}$

$\frac{cos3AcosA + sin3AsinA}{sinAcosA}$

From here, remember the following identity:

$cos(X - Y) = cosXcosY + sinXsinY$

If we set $X = 3A$ and $Y = A$, we get the following:

$cos(3A - A) = cos2A = cos3AcosA + sin3AsinA$

we can then plug this back into our original equation:

$\frac{cos2A}{sinAcosA}$

From here, remember the following identity:

$cos2A = cos^{2}A - sin^{2}A$

we can then plug this back into our original equation:

$\frac{cos^{2}A - sin^{2}A}{sinAcosA}$

$\frac{cos^{2}A}{sinAcosA} - \frac{sin^{2}A}{sinAcosA}$

$\frac{cosA}{sinA} - \frac{sinA}{cosA}$

$cotA - tanA$