Everything Maths Grade 11

CHAPTER 17. TRIGONOMETRY 17.3

Example 1: Trigonometric Identities A

QUESTION

Simplify using identities:

1. tan^2 θ. cos^2 θ
   2.cos^12 θ− tan^2 θ

SOLUTION

Step 1 : Use known identities to replace tan θ

= tan^2 θ. cos^2 θ

=

sin^2 θ

cos^2 θ

. cos^2 θ

= sin^2 θ

Step 2 : Use known identities to replace tan θ

=

1

cos^2 θ

− tan^2 θ

=

1

cos^2 θ

−

sin^2 θ

cos^2 θ

=

1 − sin^2 θ

cos^2 θ

=

cos^2 θ

cos^2 θ

= 1

Example 2: Trigonometric Identities B

QUESTION

Prove:^1 −cossin x x=1+sincos x x