Using a calculator we find sec^2 45^∘= and 3 tan45^∘-1= We also find sec^2 225^∘= and 3 tan22

step 1 All right, in this problem, they ask us for a couple of trig functions with specific input. So,

Using a calculator we find sec^2 45^∘= and 3 tan45^∘-1= We...

Using a calculator we find $\sec ^{2} 45^{\circ}=$ ____ and $3 \tan 45^{\circ}-1=$ ____ We also find $\sec ^{2} 225^{\circ}=$ _____ and $3 \tan 225^{\circ}-1=$ _____ Is the equation $\sec ^{2} \theta=3 \tan \theta-1$ an identity?

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Key Concepts

Verification of Identities

This concept involves the process of determining whether an equation is an identity, meaning it holds true for all permissible values of the variable. It often entails substituting specific angle values into both sides of the equation to check for consistency, which is a practical method for confirming or refuting a proposed identity.

Trigonometric Functions

This concept involves understanding the definitions and relationships of functions like secant and tangent. Secant is the reciprocal of cosine while tangent is the ratio of sine to cosine, and these definitions form the basis for evaluating trigonometric expressions.

Trigonometric Identities

Trigonometric identities are equations that hold true for all values where the functions are defined. A common example is the identity sec²? = 1 + tan²?, which serves as a foundational tool in verifying and deriving other relationships among trigonometric functions.

Special Angles in Trigonometry

Special angles, such as 45° and 225°, have known exact trigonometric values that simplify calculations. These angles are often chosen for testing identities because their sine, cosine, tangent, and secant values are explicit and well-understood, facilitating the verification process.

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