Simplifying the Equation | tan^2(theta) + 1 = sec^2(theta)

tan^2(theta)+1 =

The equation you have given, tan^2(theta) + 1, can be simplified further using a trigonometric identity

The equation you have given, tan^2(theta) + 1, can be simplified further using a trigonometric identity.

In trigonometry, there is a Pythagorean identity that states:
sin^2(theta) + cos^2(theta) = 1

Using this identity, we can rewrite the equation by replacing tan^2(theta) with sin^2(theta) / cos^2(theta):

sin^2(theta) / cos^2(theta) + 1

Now, we can combine the two fractions by finding a common denominator:

(sin^2(theta) + cos^2(theta)) / cos^2(theta)

Since sin^2(theta) + cos^2(theta) equals 1 (according to the Pythagorean identity):

1 / cos^2(theta)

To simplify further, we can use another trigonometric identity:

cos^2(theta) = 1 / sec^2(theta)

Substituting this into our equation:

1 / (1 / sec^2(theta))

Flipping the fraction:

sec^2(theta)

Therefore, the simplified form of tan^2(theta) + 1 is sec^2(theta).

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