Trig Identities

1. What is the value of sin2x + cos2x?

1

0

2

-1

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

-1

2

1

0

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.

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

-1

0

2

1

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.

4. Which trigonometric functions are considered even identities?

Cot, sec

Cos, sec

Tan, cot

Sin, csc

Even identities are functions for which f(-x) = f(x). In this case, cos(-x) = cos(x) and sec(-x) = sec(x), making them even identities.

Explanation

Even identities are functions for which f(-x) = f(x). In this case, cos(-x) = cos(x) and sec(-x) = sec(x), making them even identities.

5. What is the trigonometric function of sin(π/2 - x)?

Tan x

Sin x

Cot x

Cos x

When dealing with sine and cosine of complementary angles, we use the co-function identity, which states that sin(π/2 - x) = cos x.

Explanation

When dealing with sine and cosine of complementary angles, we use the co-function identity, which states that sin(π/2 - x) = cos x.