What is the general solution for 7sin(x)cos(x)+cos^2(x)=1 ?

The general solution for 7sin(x)cos(x)+cos^2(x)=1 is x=2pin,x=pi+2pin,x=1.42889…+pin

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7sin(x)cos(x)+cos^2(x)=1

7 sin (x) cos (x) + cos^{2} (x) = 1

x = 2 πn, x = π + 2 πn, x = 1.42889 \dots + πn

Solution steps

7 sin (x) cos (x) + cos^{2} (x) = 1

Subtract

1

from both sides

7 sin (x) cos (x) + cos^{2} (x) - 1 = 0

Rewrite using trig identities

- sin^{2} (x) + 7 cos (x) sin (x) = 0

Factor

- sin^{2} (x) + 7 cos (x) sin (x) : sin (x) (- sin (x) + 7 cos (x))

sin (x) (- sin (x) + 7 cos (x)) = 0

Solving each part separately

sin (x) = 0 or - sin (x) + 7 cos (x) = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

- sin (x) + 7 cos (x) = 0 : x = arctan (7) + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arctan (7) + πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = 1.42889 \dots + πn

(tan (x) - 1) (cos (x) - 1) = 0

sin (y) = \frac{4}{12}

x, 2 y sin (x) = 0

2 sin^{2} (\frac{θ}{2}) - 2 cos^{2} (θ) = 0

- 14 sin (x) + 14 cos (2 x) = 0

What is the general solution for 7sin(x)cos(x)+cos^2(x)=1 ?
The general solution for 7sin(x)cos(x)+cos^2(x)=1 is x=2pin,x=pi+2pin,x=1.42889…+pin