Prove the following trigonometric identities. 1. (csc t + cott)(1 – cos t) = sin t 2. sin? 0 – sin² ø + cos² 0 sin² ¢ – sin² 0 cos² $ = 0 3. (1+sinx)²+cos² x = 2 1+sinx

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 62E
Question
100%
Prove the following trigonometric identities.
1. (csc t + cot t)(1 – cos t) = sin t
2. sin? 0 – sin² ¢ + cos² 0 sin² ¢ – sin? 0 cos² ¢ = 0
(1+sin x)²+cos² x
3.
= 2
1+sin x
(tan x+tan y
4. cot y
= tan x
.cotx+cot y.
sin 4t-sin 2t
5.
cos4t-cos 2t
= tan t
Transcribed Image Text:Prove the following trigonometric identities. 1. (csc t + cot t)(1 – cos t) = sin t 2. sin? 0 – sin² ¢ + cos² 0 sin² ¢ – sin? 0 cos² ¢ = 0 (1+sin x)²+cos² x 3. = 2 1+sin x (tan x+tan y 4. cot y = tan x .cotx+cot y. sin 4t-sin 2t 5. cos4t-cos 2t = tan t
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