How to verify an identity without finding the LCD

The video tutorial explains how to verify a trigonometric identity involving sine, cosecant, cosine, and secant. The instructor begins by introducing the identity and discussing the need to work with rational expressions and common denominators. By applying reciprocal identities, the expression is simplified, leading to the verification of the identity using the Pythagorean identity. The tutorial concludes with the confirmation that the identity holds true.

What is the initial trigonometric identity that needs to be verified?

• sine of X divided by cosecant of X plus cosine of X divided by secant of X equals 1

• sine of X times cosine of X equals 1

• sine of X plus cosine of X equals 1

• sine squared of X plus cosine squared of X equals 1

What is the least common denominator (LCD) used in the simplification process?

• sine squared of X plus cosine squared of X

• sine of X times cosine of X

• cosecant of X plus secant of X

• cosecant of X times secant of X

Which identity is used to rewrite sine of X divided by cosecant of X?

• sine of X times sine of X

• cosine of X times cosine of X

• sine of X times 1 over cosecant of X

• cosine of X times 1 over secant of X

What is the result of applying the reciprocal identities to the expression?

• sine squared of X plus cosine squared of X equals 1

• sine of X plus cosine of X equals 1

• sine of X times cosine of X equals 1

• sine of X divided by cosine of X equals 1

Which identity confirms that the original trigonometric expression equals 1?

• Quotient identity

• Reciprocal identity

• Pythagorean identity

• Even-Odd identity