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

The general solution for sec^2(x)+cot^2(x)=csc^2(x) is No Solution for x\in\mathbb{R}

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sec^2(x)+cot^2(x)=csc^2(x)

sec^{2} (x) + cot^{2} (x) = csc^{2} (x)

No Solution for x \in R

Solution steps

sec^{2} (x) + cot^{2} (x) = csc^{2} (x)

Subtract

csc^{2} (x)

from both sides

sec^{2} (x) + cot^{2} (x) - csc^{2} (x) = 0

Rewrite using trig identities

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

Move

1

to the right side

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

Move

1

to the right side

tan^{2} (x) = 0

Apply rule

x^{n} = 0 \Rightarrow x = 0

tan (x) = 0

General solutions for

tan (x) = 0

x = 0 + πn

Solve

x = 0 + πn : x = πn

x = πn

Since the equation is undefined for:

πn

No Solution for x \in R

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sin (x) = \frac{1}{2}, 0 < x < \frac{π}{2}

sin (2 x) = cos (8 x)

What is the general solution for sec^2(x)+cot^2(x)=csc^2(x) ?
The general solution for sec^2(x)+cot^2(x)=csc^2(x) is No Solution for x\in\mathbb{R}