What is the general solution for tan(x)+cot(x)=2sec(x) ?

The general solution for tan(x)+cot(x)=2sec(x) is x= pi/6+2pin,x=(5pi)/6+2pin

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tan(x)+cot(x)=2sec(x)

tan (x) + cot (x) = 2 sec (x)

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

tan (x) + cot (x) = 2 sec (x)

Subtract

2 sec (x)

from both sides

tan (x) + cot (x) - 2 sec (x) = 0

Express with sin, cos

\frac{cos ^{2} ( x ) + ( - 2 + sin ( x ) ) sin ( x )}{cos ( x ) sin ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Rewrite using trig identities

1 - 2 sin (x) = 0

Move

1

to the right side

- 2 sin (x) = - 1

Divide both sides by

- 2

sin (x) = \frac{1}{2}

General solutions for

sin (x) = \frac{1}{2}

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

12 sin^{2} (θ) = 9

2 cos (x) + 3 = 0, 0 \leq x \leq 2 π

\frac{cot ^{2} ( x )}{1 + sin ( x )} = \frac{csc ( x ) - 1}{sin ^{2} ( x )}

tan (x) = 2.3

2 sec^{2} (x) = 5 tan (x) + 5

What is the general solution for tan(x)+cot(x)=2sec(x) ?
The general solution for tan(x)+cot(x)=2sec(x) is x= pi/6+2pin,x=(5pi)/6+2pin