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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