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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

cot (\frac{π}{2} - x) = tan (x)

\frac{1 - cos ^{2} ( x )}{sin ( x )} = sin (x)

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

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

\frac{1}{cos ^{2} ( x )} = sec^{2} (x)

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