What is the general solution for 4tan^2(x)+15sec(x)=0 ?

The general solution for 4tan^2(x)+15sec(x)=0 is x=1.82347…+2pin,x=-1.82347…+2pin

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4tan^2(x)+15sec(x)=0

4 tan^{2} (x) + 15 sec (x) = 0

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

Solution steps

4 tan^{2} (x) + 15 sec (x) = 0

Rewrite using trig identities

(- 1 + sec^{2} (x)) \cdot 4 + 15 sec (x) = 0

Solve by substitution

sec (x) = \frac{1}{4}, sec (x) = - 4

sec (x) = \frac{1}{4} :

No Solution

sec (x) = - 4 : x = arcsec (- 4) + 2 πn, x = - arcsec (- 4) + 2 πn

Combine all the solutions

x = arcsec (- 4) + 2 πn, x = - arcsec (- 4) + 2 πn

Show solutions in decimal form

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

sin^{4} (x) + cos^{4} (x) = cos^{4} (x)

cot (x) = \frac{40}{32}

tan (a) = \frac{3}{8}

sin (2 x + 10) = cos (3 x - 20)

sin^{3} (x) = - \frac{2}{3}

What is the general solution for 4tan^2(x)+15sec(x)=0 ?
The general solution for 4tan^2(x)+15sec(x)=0 is x=1.82347…+2pin,x=-1.82347…+2pin