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Home > PC > Chapter 4 > Lesson 4.2.4 > Problem 4-112

4-112.
  1. Verify the following trigonometric identities. Intermediate steps may involve complex fractions. Homework Help ✎

    1. cot2 x(sec2 x − 1) = 1

    2. sin2 α − cos2 α = 1 − 2 cos2 α

    3. tan2 β + 6 = sec2 β + 5

    4. cos y + sin y · tan y = sec y

Substitute a Pythagorean Identity for sec2x.

Substitute the Fundamental Pythagorean Identity into the left side of the equation for sin2α.

Substitute a Pythagorean Identity for sec2x.

Rewrite tan y as sin y / cos y.
Get common denominators and simplify.