What is the general solution for 2sin(x)+cos(x)=3^3 ?

The general solution for 2sin(x)+cos(x)=3^3 is No Solution for x\in\mathbb{R}

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

2 sin (x) + cos (x) = 3^{3}

No Solution for x \in R

Solution steps

2 sin (x) + cos (x) = 3^{3}

Subtract

cos (x)

from both sides

2 sin (x) = 27 - cos (x)

Square both sides

(2 sin (x))^{2} = (27 - cos (x))^{2}

Subtract

(27 - cos (x))^{2}

from both sides

4 sin^{2} (x) - 729 + 54 cos (x) - cos^{2} (x) = 0

Rewrite using trig identities

- 725 + 54 cos (x) - 5 cos^{2} (x) = 0

Solve by substitution

cos (x) = \frac{27}{5} - i \frac{4 181}{5}, cos (x) = \frac{27}{5} + i \frac{4 181}{5}

cos (x) = \frac{27}{5} - i \frac{4 181}{5} :

No Solution

cos (x) = \frac{27}{5} + i \frac{4 181}{5} :

No Solution

Combine all the solutions

No Solution

Verify solutions by plugging them into the original equation

No Solution for x \in R

What is the general solution for 2sin(x)+cos(x)=3^3 ?
The general solution for 2sin(x)+cos(x)=3^3 is No Solution for x\in\mathbb{R}