Trigonometric Identities and Simplifications

This video tutorial covers the verification of 14 trigonometric identity problems. It begins with an introduction to the process of verifying identities, followed by step-by-step solutions to each problem. The tutorial emphasizes the use of Pythagorean identities, cofunctions, and even/odd identities, as well as techniques like factoring and finding common denominators. The instructor encourages viewers to attempt solving the problems independently and provides guidance on how to approach each problem logically.

What is the first step in verifying a trigonometric identity?

• Add a constant to both sides.

• Start with the simpler side and expand.

• Start with the more complex side and simplify.

• Multiply both sides by a constant.

In the first identity problem, what identity is used to replace cosecant squared theta minus 1?

• Sine squared theta

• Cotangent squared theta

• Cosine squared theta

• Tangent squared theta

What is the common denominator used in the second identity problem?

• 1 - sine theta

• 1 + sine theta

• 1 - cosine theta

• 1 + cosine theta

In the third identity problem, what substitution is made for sine squared theta minus 1?

• Negative cosine squared theta

• Cotangent squared theta

• Cosine squared theta

• Tangent squared theta

What technique is used in the fourth identity problem to simplify the expression?

• Multiplying by the conjugate

• Adding a constant

• Using a reciprocal identity

• Factoring

In the fifth identity problem, what is factored out as the greatest common factor?

• Cosine squared theta

• Cosecant squared theta

• Cotangent squared theta

• Sine squared theta

What is the result of combining the fractions in the sixth identity problem?

• Two secant theta

• Two cotangent theta

• Two cosecant theta

• Two tangent theta

In the seventh identity problem, what is the cofunction of cotangent of pi/2 minus theta?

• Secant of theta

• Sine of theta

• Cosine of theta

• Tangent of theta

What identity is used to simplify the expression in the ninth identity problem?

• Reciprocal identity

• Pythagorean identity

• Cofunction identity

• Even and odd identity

In the tenth identity problem, what is the result of foiling the expression?

• Cotangent squared theta

• Sine squared theta

• Cosine squared theta

• Tangent squared theta