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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