What is the general solution for (sec^2(+1))(sec^2(-1))=tan(x) ?

The general solution for (sec^2(+1))(sec^2(-1))=tan(x) is x=1.48578…+pin

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(sec^2(+1))(sec^2(-1))=tan(x)

(sec^{2} (+ 1)) (sec^{2} (- 1)) = tan (x)

x = 1.48578 \dots + πn

Degrees

x = 85.12895 \dots^{\circ} + 18 0^{\circ} n

Solution steps

(sec^{2} (1)) (sec^{2} (- 1)) = tan (x)

sec (- 1) = sec (1)

sec (- 1)

Use the following property:

sec (- x) = sec (x)

sec (- 1) = sec (1)

= sec (1)

sec^{2} (1) sec^{2} (1) = tan (x)

Switch sides

tan (x) = sec^{2} (1) sec^{2} (1)

Simplify

sec^{2} (1) sec^{2} (1) : sec^{4} (1)

sec^{2} (1) sec^{2} (1)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

sec^{2} (1) sec^{2} (1) = sec^{2 + 2} (1)

= sec^{2 + 2} (1)

Add the numbers:

2 + 2 = 4

= sec^{4} (1)

Apply trig inverse properties

tan (x) = sec^{4} (1)

General solutions for

tan (x) = sec^{4} (1)

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (sec^{4} (1)) + πn

x = arctan (sec^{4} (1)) + πn

Show solutions in decimal form

x = 1.48578 \dots + πn

2 cos^{2} (x) - 8 cos (x) = 2 sin^{2} (x) - 5

2 cos^{2} (a) tan (a) = tan (a)

sin^{2} (x) + 5 sin (x) + 5 = 0

cos (x) = - 0.814

3 cos^{2} (x) - 8 cos (x) + 4 = sin^{2} (x)

What is the general solution for (sec^2(+1))(sec^2(-1))=tan(x) ?
The general solution for (sec^2(+1))(sec^2(-1))=tan(x) is x=1.48578…+pin