simplify sin(45-a)

Solution

simplify

sin (4 5^{\circ} - a)

\frac{2 cos ( a ) - 2 sin ( a )}{2}

Solution steps

sin (4 5^{\circ} - a)

Rewrite using trig identities

= \frac{2 cos ( a ) - 2 sin ( a )}{2}

cos^{2} (9 0^{\circ} - θ)

sec (15 π - x)

25 - (5 sin (x))^{2}

- \frac{sin ( a )}{sin ( - a )}

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

What is sin(45-a) ?
The solution to sin(45-a) is (sqrt(2)cos(a)-sqrt(2)sin(a))/2