1. (1 cos 0) (1 + cos 0) (1 + cot²0) = 1 1 1 secx - 1 secx + 1 2. 2 cotx csc x + 3. sin²xcos5x = cos x(sin²x - 2sin^x + sinºx)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.4: Multiple-angle Formulas
Problem 40E
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Prove the given identities.

1.
2.
4.
(1 − cos 0) (1 + cos 0) (1 + cot²0) = 1
1
1
+
secx - 1 secx + 1
3. sin²xcos 5x = cos x(sin²x - 2sin¹x + sinºx)
5.
2 cotx csc x =
sin x
COS X
sin x + cos x
2 tan x
1 - tan²x
+
=
2 sin ²x - 1
22
1 + 2 sin x cos x
1
cos x + sin x
cos²x1 COSX
sin x
=
Transcribed Image Text:1. 2. 4. (1 − cos 0) (1 + cos 0) (1 + cot²0) = 1 1 1 + secx - 1 secx + 1 3. sin²xcos 5x = cos x(sin²x - 2sin¹x + sinºx) 5. 2 cotx csc x = sin x COS X sin x + cos x 2 tan x 1 - tan²x + = 2 sin ²x - 1 22 1 + 2 sin x cos x 1 cos x + sin x cos²x1 COSX sin x =
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