Question

8 sec square theta - 8 tan square theta​

Answer 1

Answer:

8

8 sec square theta - 8 tan square theta

8 ( sec square theta - tan square theta )

8 × 1

8

formula,

sec square x - tan square x = 1

Answer 2

Answer:

The simplified expression is 8.

Step-by-step explanation:

A trigonometric identity is an equation that involves trigonometric functions that holds true for all values of the variables involved. These identities are useful in simplifying and solving mathematical problems involving trigonometric functions.

There are many trigonometric identities, including Pythagorean identities, reciprocal identities, quotient identities, and co-function identities. For example, the Pythagorean identity states that sin^2(x) + cos^2(x) = 1 for all values of x, where sin(x) and cos(x) are the sine and cosine functions, respectively.

Trigonometric identities are often used in calculus, physics, and engineering, as well as in other fields that involve wave phenomena. They are also important in the study of triangles and other geometrical shapes, where they can be used to solve problems involving angles and lengths of sides.

To simplify the expression 8 sec²θ - 8 tan²θ, we can start by using the trigonometric identity:

tan²θ + 1 = sec²θ

Rearranging this identity, we get:

sec²θ - tan²θ = 1

Substituting this into the original expression, we get:

8(sec²θ - tan²θ) = 8(1) = 8

Therefore, the simplified expression is 8.

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