What is sin(90-(a-b)) ?

The solution to sin(90-(a-b)) is cos(a-b)

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simplify sin(90-(a-b))

simplify

sin (9 0^{\circ} - (a - b))

cos (a - b)

Solution steps

sin (9 0^{\circ} - (a - b))

Rewrite using trig identities

= cos (a) cos (b) + sin (a) sin (b)

Use the Angle Difference identity:

cos (s) cos (t) + sin (s) sin (t) = cos (s - t)

= cos (a - b)

sin (t - π) + sin (t - 2 π)

sin (\frac{θ}{2} - 9 0^{\circ})

sin^{5} (- x)

sin (\frac{π}{15} (- x) - 0.25)

cot (x + 4 5^{\circ})