Is prove-tan^2(x)=1-sec^2(x) ?

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

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

prove

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

True

Solution steps

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

Manipulating right side

1 - sec^{2} (x)

Rewrite using trig identities

1 - sec^{2} (x)

Use the Pythagorean identity:

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

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

= - tan^{2} (x)

= - tan^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{cot ^{2} ( x )}{csc ^{2} ( x )} = cos^{2} (x)

(cos (x) - sin (x)) 2 = 1 - 2 sin (x) cos (x)

cos (x) (csc^{2} (x)) = cot (x) csc (x)

sin (x) cos (x) csc^{2} (x) = cot (x)

4 cos^{2} (x) - 2 = 0

Is prove-tan^2(x)=1-sec^2(x) ?
The answer to whether prove-tan^2(x)=1-sec^2(x) is True