Question

Use trigonometric identities to transform the left side of the equation into the right side (0 < < /2).

Answer 1

All the missing elements derived from trigonometric and algebraic procedures are listed below:

1. tan² θ
2. sin² θ
3. cos² θ

How to prove a trigonometric expression

In this question we need to prove that the trigonometric expression (sec θ + tan θ) · (sec θ - tan θ) is equal to 1 by algebraic and trigonometric properties. The complete procedure is shown below:

(sec θ + tan θ) · (sec θ - tan θ)        Given

sec² θ - tan² θ                                  Difference of squares

1 / cos² θ - sin² θ / cos² θ                Definitions of secant and tangent

(1 - sin² θ) / cos² θ                            Subtraction of fraction with same denominator

cos² θ / cos ² θ                                sin² θ + cos² θ = 1

1                                                        Definition of division / Existence of multiplicative inverse / Modulative property / Result

All the missing elements derived from trigonometric and algebraic procedures are listed below:

1. tan² θ
2. sin² θ
3. cos² θ

To learn more on trigonometric expressions: https://brainly.com/question/11919000

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