Mastering Trigonometric Identities Quiz

1) What is the value of sin2x + cos2x?

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The trigonometric identity sin^2(x) + cos^2(x) = 1 is known as the Pythagorean identity, which holds true for all values of x in trigonometry.

Explanation

The trigonometric identity sin^2(x) + cos^2(x) = 1 is known as the Pythagorean identity, which holds true for all values of x in trigonometry.

2) Simplify the expression csc^2(x) - cot^2(x).

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To simplify the expression csc^2(x) - cot^2(x), we can use the fundamental trigonometric identities csc(x) = 1/sin(x) and cot(x) = 1/tan(x). By substituting these identities into the expression and simplifying further, we arrive at the result of 1.

Explanation

To simplify the expression csc^2(x) - cot^2(x), we can use the fundamental trigonometric identities csc(x) = 1/sin(x) and cot(x) = 1/tan(x). By substituting these identities into the expression and simplifying further, we arrive at the result of 1.

3) What is the value of sec^2(x) - tan^2(x)?

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The identity sec^2(x) - tan^2(x) = 1 is based on the Pythagorean identities for trigonometric functions. Secant and tangent are reciprocal functions in terms of sine and cosine, leading to the simplification to 1.

Explanation

The identity sec^2(x) - tan^2(x) = 1 is based on the Pythagorean identities for trigonometric functions. Secant and tangent are reciprocal functions in terms of sine and cosine, leading to the simplification to 1.