Proving the Trigonometric Identity sec^2x = 1 + tan^2x in Math

1 + tan^2x =

sec^2x

sec^2x

To solve this question, we can start with the left side of the equation and use the trigonometric identity:

1 + tan^2x = sec^2x

We know that tan^2x + 1 = sec^2x from the Pythagorean identity. Therefore, we can substitute tan^2x + 1 in the left side of the equation:

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

Then we simplify:

1 + tan^2x = 1 + 2tan^2x

1 + tan^2x = (1/cos^2x) * cos^2x + tan^2x

1 + tan^2x = (1 + tan^2x) / cos^2x

Finally, we can simplify further:

1 + tan^2x = sec^2x

Therefore, the left side of the equation is equal to the right side of the equation, which proves the trigonometric identity.

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