Is cot^2(x)+csc^2(x)=1+2cot^2(x) ?

The answer to whether cot^2(x)+csc^2(x)=1+2cot^2(x) is True

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prove cot^2(x)+csc^2(x)=1+2cot^2(x)

prove

cot^{2} (x) + csc^{2} (x) = 1 + 2 cot^{2} (x)

True

Solution steps

cot^{2} (x) + csc^{2} (x) = 1 + 2 cot^{2} (x)

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

csc^{2} (x) = 1 + cot^{2} (x)

= cot^{2} (x) + 1 + cot^{2} (x)

Simplify

cot^{2} (x) + 1 + cot^{2} (x) : 2 cot^{2} (x) + 1

cot^{2} (x) + 1 + cot^{2} (x)

Group like terms

= cot^{2} (x) + cot^{2} (x) + 1

Add similar elements:

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

= 2 cot^{2} (x) + 1

= 2 cot^{2} (x) + 1

= 2 cot^{2} (x) + 1

= 1 + 2 cot^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

Is cot^2(x)+csc^2(x)=1+2cot^2(x) ?
The answer to whether cot^2(x)+csc^2(x)=1+2cot^2(x) is True