What is the general solution for 3sin(x)+4=5cos(x),[0.2pi] ?

The general solution for 3sin(x)+4=5cos(x),[0.2pi] is No Solution for x\in\mathbb{R}

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3sin(x)+4=5cos(x),[0.2pi]

3 sin (x) + 4 = 5 cos (x), [0.2 π]

No Solution for x \in R

Solution steps

3 sin (x) + 4 = 5 cos (x), [0.2 π]

Square both sides

(3 sin (x) + 4)^{2} = (5 cos (x))^{2}

Subtract

(5 cos (x))^{2}

from both sides

(3 sin (x) + 4)^{2} - 25 cos^{2} (x) = 0

Rewrite using trig identities

- 9 + 24 sin (x) + 34 sin^{2} (x) = 0

Solve by substitution

sin (x) = \frac{3 ( 5 2 - 4 )}{34}, sin (x) = - \frac{3 ( 4 + 5 2 )}{34}

sin (x) = \frac{3 ( 5 2 - 4 )}{34}, [0.2 π] :

No Solution

sin (x) = - \frac{3 ( 4 + 5 2 )}{34}, [0.2 π] :

No Solution

Combine all the solutions

No Solution

Verify solutions by plugging them into the original equation

No Solution for x \in R

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What is the general solution for 3sin(x)+4=5cos(x),[0.2pi] ?
The general solution for 3sin(x)+4=5cos(x),[0.2pi] is No Solution for x\in\mathbb{R}