Is tan^2(x)+4=sec^2(x)+3 ?

The answer to whether tan^2(x)+4=sec^2(x)+3 is True

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prove tan^2(x)+4=sec^2(x)+3

prove

tan^{2} (x) + 4 = sec^{2} (x) + 3

True

Solution steps

tan^{2} (x) + 4 = sec^{2} (x) + 3

Manipulating left side

tan^{2} (x) + 4

Rewrite using trig identities

tan^{2} (x) + 4

Use the Pythagorean identity:

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

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

= sec^{2} (x) - 1 + 4

Simplify

= sec^{2} (x) + 3

= sec^{2} (x) + 3

We showed that the two sides could take the same form

\Rightarrow True

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

sin (x - \frac{π}{2}) = cos (x)

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

sec (x) sin (x) cot (x) = 1

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