What is the general solution for 7cos(x)tan(x)-5tan(x)=0 ?

The general solution for 7cos(x)tan(x)-5tan(x)=0 is x=pin,x=0.77519…+2pin,x=2pi-0.77519…+2pin

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7cos(x)tan(x)-5tan(x)=0

7 cos (x) tan (x) - 5 tan (x) = 0

x = πn, x = 0.77519 \dots + 2 πn, x = 2 π - 0.77519 \dots + 2 πn

Solution steps

7 cos (x) tan (x) - 5 tan (x) = 0

Factor

7 cos (x) tan (x) - 5 tan (x) : tan (x) (7 cos (x) - 5)

tan (x) (7 cos (x) - 5) = 0

Solving each part separately

tan (x) = 0 or 7 cos (x) - 5 = 0

tan (x) = 0 : x = πn

7 cos (x) - 5 = 0 : x = arccos (\frac{5}{7}) + 2 πn, x = 2 π - arccos (\frac{5}{7}) + 2 πn

Combine all the solutions

x = πn, x = arccos (\frac{5}{7}) + 2 πn, x = 2 π - arccos (\frac{5}{7}) + 2 πn

Show solutions in decimal form

x = πn, x = 0.77519 \dots + 2 πn, x = 2 π - 0.77519 \dots + 2 πn

sec^{2} (x) - 6 sec (x) = 0

9 sec^{2} (x) tan (x) = 12 tan (x)

cos (x) = - \frac{4}{7}

(8 cos (θ) - 4) (5 sin (θ) - 5) = 0

arctan (x) = \frac{π}{3}

What is the general solution for 7cos(x)tan(x)-5tan(x)=0 ?
The general solution for 7cos(x)tan(x)-5tan(x)=0 is x=pin,x=0.77519…+2pin,x=2pi-0.77519…+2pin