How to use the pythagorean identities to simplify a trigonometric expression

The video tutorial discusses transforming trigonometric expressions, focusing on converting secant squared to tangent squared using trigonometric identities. The instructor emphasizes the importance of rewriting expressions in terms of sine and cosine for simplification. The process involves using the identity secant squared equals one plus tangent squared, allowing the expression to be simplified to sine squared. The tutorial highlights the ease of canceling terms when expressions are in sine and cosine form.

What is the initial approach discussed for transforming cosine squared?

• Using the double angle formula

• Using the Pythagorean identity

• Using the angle addition formula

• Using the sum-to-product identities

Which trigonometric identity is used to transform secant squared minus one?

• Sine squared plus cosine squared equals one

• One plus tangent squared equals secant squared

• Cosine squared equals one minus sine squared

• Tangent squared equals sine squared over cosine squared

How is secant squared minus one rewritten in terms of another trigonometric function?

• As sine squared

• As cotangent squared

• As cosine squared

• As tangent squared

What is the final result after simplifying the expression using trigonometric identities?

• Secant squared

• Sine squared

• Tangent squared

• Cosine squared

Why is it beneficial to rewrite trigonometric functions in terms of sine and cosine?

• It eliminates the need for identities

• It simplifies the expression

• It makes the expression more complex

• It introduces new variables