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

The general solution for sec^2(x)-tan^2(x)=cos(x) is x=2pin

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sec^2(x)-tan^2(x)=cos(x)

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

x = 2 πn

Degrees

x = 0^{\circ} + 36 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

= 1

1 = cos (x)

Switch sides

cos (x) = 1

General solutions for

cos (x) = 1

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = 0 + 2 πn

x = 0 + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

x, cos^{2} (x) - sin^{2} (x) = 0

cos (x) = \frac{60}{61}, cos (2 x)

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

arcsin (\frac{x}{3 ^{2} + x ^{2}}) = 0.01117

cot (x) - 3 = csc (x)

What is the general solution for sec^2(x)-tan^2(x)=cos(x) ?
The general solution for sec^2(x)-tan^2(x)=cos(x) is x=2pin