What is 2sin(x-30)+cos(x) ?

The solution to 2sin(x-30)+cos(x) is sqrt(3)sin(x)

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simplify 2sin(x-30)+cos(x)

simplify

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

3 sin (x)

Solution steps

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

Rewrite using trig identities

= 2 (\frac{3}{2} sin (x) - \frac{1}{2} cos (x)) + cos (x)

Simplify

2 (\frac{3}{2} sin (x) - \frac{1}{2} cos (x)) + cos (x) : 3 sin (x)

= 3 sin (x)

sec (x - \frac{π}{4})

cos (- a)

sin (tan^{(- 1)} (x))

tan (arccos (\frac{x}{9}))

cos (2 x + \frac{2 π}{3})