05.01 Using Fundamental Identities
Question 2
Use basic identities to simplify the expression.
sin θ cos θ sec θ csc θ
a) sec^2 θ
b)csc^2 θ
c) 1
d) tan^2 θ
Answers
Answer:
Examples, solutions, videos, and lessons to help High School Algebra 2 students learn to use trigonometric identities to simplify trigonometric expressions. In these lessons, we will learn how to use trigonometric identities to simplify trigonometric expressions.
The following are some common trigonometric identities: Reciprocal Identities, Quotient Identities and Pythagorean Identities. Scroll down the page for examples and solutions using the identities to simply trigonometric expressions.
Step-by-step explanation:
Simplify sinθsecθcos2θ
Solution:
sinθsecθcos2θ=sinθsecθcosθcosθ
=tanθ⋅secθcosθ
= tan θ • sec2 θ
= tan θ (tan2 θ + 1)
= tan3 θ + tan θ
Example:
Simplify sin2θcosθ+cos2θcosθ
Solution:
sin2θcosθ+cos2θcosθ
=sin2θ+cos2θcosθ
=1cosθ
= sec θ