Pre-Calculus - how to add two trigonometric expressions without finding the LCD

The video tutorial addresses the challenge of adding fractions involving trigonometric functions, specifically cosecant and secant. It introduces an alternative approach using reciprocal identities to simplify the expression. By rewriting the terms and applying Pythagorean identities, the expression is simplified to a basic form. The tutorial concludes with a summary of the simplification process.

What is the first step in adding fractions involving trigonometric functions like cosecant and secant?

• Find a common numerator

• Multiply by the reciprocal

• Find a common denominator

• Add the numerators directly

How can the expression involving sine and cosecant be rewritten using reciprocal identities?

• As cosine times secant

• As cosecant times cosecant

• As sine times sine

• As tangent times cotangent

Which method involves multiplying by secant over secant and cosecant over cosecant?

• Graphical method

• Numerical method

• Algebraic method

• Reciprocal method

What identity is used to simplify the expression to its final form?

• Reciprocal identity

• Quotient identity

• Pythagorean identity

• Even-Odd identity

What is the result of applying the Pythagorean identity to the expression?

• Cosine of X

• Zero

• One

• Sine of X