Trigonometric Identities and Simplifications

Professor Dave explains the process of verifying trigonometric identities, starting with simple examples and progressing to more complex ones. He outlines strategies such as rewriting identities, using known identities, and manipulating fractions. The video emphasizes the importance of algebraic manipulation and practice in mastering this topic.

What is the first step in verifying the identity cosecant X times tangent X equals secant X?

• Rewrite cosecant X as one over sine X

• Rewrite cosecant X as cosine X over sine X

• Rewrite tangent X as cosine X over sine X

• Rewrite secant X as sine X over cosine X

In the example where sine X tangent X plus cosine X equals secant X, what is the first trigonometric function to be rewritten?

• Tangent X

• Cosine X

• Secant X

• Sine X

What identity is used to simplify sine squared X plus cosine squared X?

• Sine squared X equals one minus cosine squared X

• Cosine squared X equals one minus sine squared X

• Tangent squared X equals secant squared X minus one

• Sine squared X plus cosine squared X equals one

Which strategy involves expressing one fraction as the sum of two fractions?

• Combining fractions

• Separating fractions

• Using complex conjugates

• Rewriting trigonometric functions

In the identity one plus tangent squared equals secant squared, what is the common denominator used to combine terms?

• Sine squared

• Cosine squared

• Secant squared

• Tangent squared

What is the result of combining the fractions one plus sine over cosine and cosine over one plus sine?

• Cosine squared over sine

• Sine squared over cosine

• Two over cosine

• One over cosine

What is the first step in simplifying the expression sine squared plus cosine squared plus cotangent squared over one plus tangent squared?

• Rewrite cotangent squared

• Simplify sine squared plus cosine squared

• Rewrite tangent squared

• Combine fractions

What is the simplified form of one plus cotangent squared?

• Sine squared

• Tangent squared

• Cosecant squared

• Secant squared

What is the reciprocal of secant squared?

• Cosine squared

• Cosecant squared

• Tangent squared

• Sine squared

What is the final simplified form of cosine squared over sine squared?

• Secant squared

• Cosecant squared

• Cotangent squared

• Tangent squared