What is the general solution for sin^2(x)+sin(x)*cos(x)+cos^2(x)=10 ?

The general solution for sin^2(x)+sin(x)*cos(x)+cos^2(x)=10 is No Solution for x\in\mathbb{R}

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sin^2(x)+sin(x)*cos(x)+cos^2(x)=10

sin^{2} (x) + sin (x) \cdot cos (x) + cos^{2} (x) = 10

No Solution for x \in R

Solution steps

sin^{2} (x) + sin (x) cos (x) + cos^{2} (x) = 10

Rewrite using trig identities

cos (x) sin (x) + 1

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

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

= 1 + \frac{sin ( 2 x )}{2}

1 + \frac{sin ( 2 x )}{2} = 10

Move

1

to the right side

1 + \frac{sin ( 2 x )}{2} = 10

Subtract

1

from both sides

1 + \frac{sin ( 2 x )}{2} - 1 = 10 - 1

Simplify

\frac{sin ( 2 x )}{2} = 9

\frac{sin ( 2 x )}{2} = 9

Multiply both sides by

2

\frac{sin ( 2 x )}{2} = 9

Multiply both sides by

2

\frac{2 sin ( 2 x )}{2} = 9 \cdot 2

Simplify

sin (2 x) = 18

sin (2 x) = 18

- 1 \leq sin (x) \leq 1

No Solution for x \in R

x, sin (x) = \frac{2}{3}

2 sin^{2} (x) = sec (x)

tan (x) = \frac{12}{6}

3 sin (θ) - 2 sin (θ) cos (θ) = 0

\frac{3}{cos ^{2} ( x )} = 3 + 2 tan^{2} (x)

What is the general solution for sin^2(x)+sin(x)*cos(x)+cos^2(x)=10 ?
The general solution for sin^2(x)+sin(x)*cos(x)+cos^2(x)=10 is No Solution for x\in\mathbb{R}