Verifying an identity by applying the Pythagorean identities

The video tutorial explains how to solve a trigonometric equation involving secant and tangent functions. The instructor begins by choosing the more complex side of the equation to simplify, using trigonometric identities to express tangent in terms of secant. The process involves rewriting the expression to eliminate tangent, applying the distributive property, and verifying the solution. The tutorial emphasizes understanding the relationship between trigonometric functions and simplifying expressions to match both sides of the equation.

What is the first step suggested by the instructor when proving a trigonometric identity?

• Use a calculator to verify

• Convert all terms to sine and cosine

• Choose the more complex side to simplify

• Start with the simpler side

Which trigonometric identity is used to relate tangent and secant in the problem?

• sin^2(x) + cos^2(x) = 1

• 1 + tan^2(x) = sec^2(x)

• tan(x) = sin(x)/cos(x)

• sec(x) = 1/cos(x)

Why does the instructor replace tangent squared with secant squared minus one?

• To make the equation more complex

• To simplify the expression using only secant

• To introduce a new variable

• To eliminate secant from the equation

What mathematical property is applied to simplify the expression in the final section?

• Identity property

• Distributive property

• Associative property

• Commutative property

What is the result after applying the distributive property and simplifying the expression?

• sec^4(x)

• sec^2(x)

• tan^2(x)

• 1