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 Sum identity:

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

= cos (a + b)

sin (arctan (e^{x}))

sin (arcsin (θ))

cos (x + 6 0^{\circ}) - (x - 60)

sin (x + 0.5 π)

cos (θ - 2 π)