What is sin(sin(x+2pi)) ?

The solution to sin(sin(x+2pi)) is sin(sin(x))

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simplify sin(sin(x+2pi))

simplify

sin (sin (x + 2 π))

sin (sin (x))

Solution steps

sin (sin (x + 2 π))

Rewrite using trig identities

= sin (sin (x))

2 cos (x) + 7 cos (4 5^{\circ} - x)

sin (x - \frac{5 π}{3})

cos (2 x + 3 0^{\circ})

cos (arctan (x \frac{1}{3}))

2 + sin (x - \frac{π}{2})