What is the general solution for 3sec^2(x)+2-8tan(x)=0 ?

The general solution for 3sec^2(x)+2-8tan(x)=0 is x=1.03037…+pin,x= pi/4+pin

Popular >

3sec^2(x)+2-8tan(x)=0

3 sec^{2} (x) + 2 - 8 tan (x) = 0

x = 1.03037 \dots + πn, x = \frac{π}{4} + πn

Solution steps

3 sec^{2} (x) + 2 - 8 tan (x) = 0

Rewrite using trig identities

5 + 3 tan^{2} (x) - 8 tan (x) = 0

Solve by substitution

tan (x) = \frac{5}{3}, tan (x) = 1

tan (x) = \frac{5}{3} : x = arctan (\frac{5}{3}) + πn

tan (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

x = arctan (\frac{5}{3}) + πn, x = \frac{π}{4} + πn

Show solutions in decimal form

x = 1.03037 \dots + πn, x = \frac{π}{4} + πn

cos (θ) - 1 = cos (2 θ)

5 tan (x) = 9 sin (x)

x, sin (\frac{π x}{4}) = y - 1

sin (θ) = \frac{12}{37}

8 tan (\frac{θ}{2}) + 8 cos (θ) tan (\frac{θ}{2}) = 1

What is the general solution for 3sec^2(x)+2-8tan(x)=0 ?
The general solution for 3sec^2(x)+2-8tan(x)=0 is x=1.03037…+pin,x= pi/4+pin