simplify cos(45-x)

Solution

simplify

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

sin (\frac{π}{4} + x)

Solution steps

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

Rewrite using trig identities

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

Factor

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

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

Rewrite using trig identities

= sin (\frac{π}{4} + x)

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

sin^{2} (18 0^{\circ} + x)

2 sin (\frac{π}{3} + D) + 6

cos (θ^{1} - θ^{2})

cos (x - \frac{7 π}{4})