What is 4sin(45+x)+3 ?

The solution to 4sin(45+x)+3 is 2(sqrt(2)cos(x)+sqrt(2)sin(x))+3

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simplify 4sin(45+x)+3

simplify

4 sin (4 5^{\circ} + x) + 3

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

Solution steps

4 sin (4 5^{\circ} + x) + 3

Rewrite using trig identities

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

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

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

Simplify

2 cos (x) + 2 sin (x) : 2 sin (x + \frac{π}{4})

= 2 \cdot 2 sin (x + \frac{π}{4}) + 3

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

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

sin (arccos (sin (x)))

- sin (2 x + \frac{π}{4})

sin (x - \frac{π}{4}) - 1

\frac{1}{cot ( θ ) sin ( - θ )}

- 3 (\frac{3 sin ( - nπ )}{πn})

What is 4sin(45+x)+3 ?
The solution to 4sin(45+x)+3 is 2(sqrt(2)cos(x)+sqrt(2)sin(x))+3