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

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

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

simplify

4 sin (2 x - \frac{π}{4}) + 3

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

Solution steps

4 sin (2 x - \frac{π}{4}) + 3

Rewrite using trig identities

= 4 \cdot \frac{2 sin ( 2 x ) - 2 cos ( 2 x )}{2} + 3

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

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

cos (- 2 π - nπ)

1 + (cot (x))^{2}

tan (45 π + x)

8 x + cos (x + π) - x^{2}

sin (arctan (\frac{t}{3}))

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