Is sec^2(x)=1+tan^2(x) ?

The answer to whether sec^2(x)=1+tan^2(x) is True

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prove sec^2(x)=1+tan^2(x)

prove

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

True

Solution steps

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

Use the Pythagorean identity:

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

\Rightarrow True

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

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

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

\frac{1 + csc ( x )}{sec ( x )} - cot (x) = cos (x)

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