simplify tan(45-x)

Solution

simplify

tan (4 5^{\circ} - x)

\frac{cos ( x ) - sin ( x )}{cos ( x ) + sin ( x )}

Solution steps

tan (4 5^{\circ} - x)

Rewrite using trig identities

= \frac{cos ( x ) - sin ( x )}{cos ( x ) + sin ( x )}

1 + cos^{2} (x - 18 0^{\circ})

sin (2 x + \frac{π}{3})

cot (arccsc (x))

tan (2 x + \frac{π}{3})

64 - 64 sin^{2} (x)

What is tan(45-x) ?
The solution to tan(45-x) is (cos(x)-sin(x))/(cos(x)+sin(x))