Body

Lesson 23 - Trigonometric Identities

Pg. 307: 3, 4, 6, 8, 9, 15, 28, 32

Lesson 23 - 7.2 # 3 - Simplify

Lesson 23 - 7.2 # 4 - Simplify

Since

Lesson 23 - 7.2 # 6 - Simplify

Since

So numerator is above

Lesson 23 - 7.2 # 8 - Simplify

Common denominator is

Perfect square or (see 7.2 #6)

Lesson 23 - 7.2 # 9 - Simplify

Common denominator is

Lesson 23 - 7.2 # 15 - Prove algebraically

Alternate way than text

Multiply both sides by sin t and (1 - cos t)

(true statement)

Lesson 23 - 7.2 # 28 - Find exact solution to:
(a)

Note cos(2x) = 2cos² x - 1

So (find similar trig identity - also note similarity between above and 2x² + x - 1, where x = cos x)

Factor:

For

For

Ans

(a)

Need common trig identity

Divide by -1

For (Q-III and Q-IV)

So or

Lesson 23 - 7.2 # 32 - Find exact solution to , if sin