Question

simplify the expression (cos4x + cos3x) / (sin4x - sin3x)

Answer 1

http://www.sosmath.com/trig/Trig5/trig5/img9.gif

\(\bf \cfrac{cos(4x)+cos(3x)}{sin(4x)-sin(3x)}\\ \quad \\ \quad \\

\cfrac{
\cancel{2cos\left(\frac{4x+3x}{2}\right)}cos\left(\frac{4x-3x}{2}\right)
}{
\cancel{2cos\left(\frac{4x+3x}{2}\right)}sin\left(\frac{4x-3x}{2}\right)
}

\implies \cfrac{cos\left(\frac{4x-3x}{2}\right)}{sin\left(\frac{4x-3x}{2}\right)}\implies tan\left(\frac{4x-3x}{2}\right)\\ \quad \\
tan\left(\frac{x}{2}\right)\)

Answer 2

hmmm actually

Answer 3

\(\bf \cfrac{cos(4x)+cos(3x)}{sin(4x)-sin(3x)}\\ \quad \\ \quad \\

\cfrac{
\cancel{2cos\left(\frac{4x+3x}{2}\right)}cos\left(\frac{4x-3x}{2}\right)
}{
\cancel{2cos\left(\frac{4x+3x}{2}\right)}sin\left(\frac{4x-3x}{2}\right)
}

\implies \cfrac{cos\left(\frac{4x-3x}{2}\right)}{sin\left(\frac{4x-3x}{2}\right)}\implies cot\left(\frac{4x-3x}{2}\right)\\ \quad \\
cot\left(\frac{x}{2}\right)\)

Answer 4

THANK YOU SOOOOOO MUCH!!!!!!!!!!! THAT IS AMAZING!!!! :D

Answer 5

how did you get 2 cos (4x+3x)/2?

Answer 6

http://www.sosmath.com/trig/Trig5/trig5/img9.gif <---- from the sum to product trigonometry identities