simplify cos(3x-45)

Solution

simplify

cos (3 x - 4 5^{\circ})

sin (\frac{π}{4} + 3 x)

Solution steps

cos (3 x - 4 5^{\circ})

Rewrite using trig identities

= \frac{2 cos ( 3 x ) + 2 sin ( 3 x )}{2}

Factor

cos (3 x) 2 + sin (3 x) 2 : 2 (cos (3 x) + sin (3 x))

= \frac{( cos ( 3 x ) + sin ( 3 x ) ) 2}{2}

Rewrite using trig identities

= sin (\frac{π}{4} + 3 x)

2 sin (\frac{π}{4} + x)

sec (θ + 72 0^{\circ})

cos (4 π - nπ)

sin (\frac{nπ}{2}) - sin (nπ)

4 cos (100 π t + π)