What is the general solution for sec^2(x)+tan(x)=1,0<= x<= 2pi ?

The general solution for sec^2(x)+tan(x)=1,0<= x<= 2pi is x=(3pi)/4 ,x=(7pi)/4

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sec^2(x)+tan(x)=1,0<= x<= 2pi

sec^{2} (x) + tan (x) = 1, 0 \leq x \leq 2 π

x = \frac{3 π}{4}, x = \frac{7 π}{4}

Solution steps

sec^{2} (x) + tan (x) = 1, 0 \leq x \leq 2 π

Subtract

1

from both sides

sec^{2} (x) + tan (x) - 1 = 0

Rewrite using trig identities

\frac{1}{cot ^{2} ( x )} + \frac{1}{cot ( x )} = 0

Solve by substitution

cot (x) = - 1

cot (x) = - 1, 0 \leq x \leq 2 π : x = \frac{3 π}{4}, x = \frac{7 π}{4}

Combine all the solutions

x = \frac{3 π}{4}, x = \frac{7 π}{4}

6 tanh^{2} (x) + 5 sech (x) - 7 = 0

2 sin (x) + 2 = 0, 0 \leq x \leq 2 π

2 cos^{2} (x) + 3 cos (x) = 2, 0 \leq x \leq 2 π

cos (θ) = \frac{7}{11}

(1 - sin^{2} (x)) \cdot 2 - 3 sin (x) = 0

What is the general solution for sec^2(x)+tan(x)=1,0<= x<= 2pi ?
The general solution for sec^2(x)+tan(x)=1,0<= x<= 2pi is x=(3pi)/4 ,x=(7pi)/4