What is 2sin(2x-pi/4)+3 ?

The solution to 2sin(2x-pi/4)+3 is sqrt(2)sin(2x)-sqrt(2)cos(2x)+3

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simplify 2sin(2x-pi/4)+3

simplify

2 sin (2 x - \frac{π}{4}) + 3

2 sin (2 x) - 2 cos (2 x) + 3

Solution steps

2 sin (2 x - \frac{π}{4}) + 3

Rewrite using trig identities

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

2 \cdot \frac{2 sin ( 2 x ) - 2 cos ( 2 x )}{2} = 2 sin (2 x) - 2 cos (2 x)

= 2 sin (2 x) - 2 cos (2 x) + 3

sin (\frac{20 π}{2} + θ)

4 - (2 cos (θ))^{2}

- cos (π + a)

cos (θ + 2 π)

2 cos^{3} (π x) + cos^{2} (π x) - 1

What is 2sin(2x-pi/4)+3 ?
The solution to 2sin(2x-pi/4)+3 is sqrt(2)sin(2x)-sqrt(2)cos(2x)+3