What is the general solution for 7cos(b)+9=3cos(b)+8 ?

The general solution for 7cos(b)+9=3cos(b)+8 is b=1.82347…+2pin,b=-1.82347…+2pin

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7cos(b)+9=3cos(b)+8

7 cos (b) + 9 = 3 cos (b) + 8

b = 1.82347 \dots + 2 πn, b = - 1.82347 \dots + 2 πn

Solution steps

7 cos (b) + 9 = 3 cos (b) + 8

Solve by substitution

cos (b) = - \frac{1}{4}

cos (b) = - \frac{1}{4} : b = arccos (- \frac{1}{4}) + 2 πn, b = - arccos (- \frac{1}{4}) + 2 πn

Combine all the solutions

b = arccos (- \frac{1}{4}) + 2 πn, b = - arccos (- \frac{1}{4}) + 2 πn

Show solutions in decimal form

b = 1.82347 \dots + 2 πn, b = - 1.82347 \dots + 2 πn

tan^{2} (θ) + sec (θ) - 2 = 0

tan (x) - 1 = - 3 + 3 cot (x)

14 cos^{2} (x) = 7

cos (2 θ) + sin (2 θ) = - 1

sin (θ) = \frac{19}{27}

What is the general solution for 7cos(b)+9=3cos(b)+8 ?
The general solution for 7cos(b)+9=3cos(b)+8 is b=1.82347…+2pin,b=-1.82347…+2pin