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•sin ² (x/2) = = (tan x sin x)/ 2tan x = sin ² (x/2) •tan x - cot x = - 2cot 2x •sin ² (x/2) = (sin x tan x/2 )/2 = sin²(x/2) •sin²x = [ 2cos ² (x/2) ] [ 1 − cos x ] = sin ²x •(2sin x - sin 2x)/(2sin x + sin 2x ) = tan² (x/2) 2

•sin ² (x/2) = = (tan x sin x)/ 2tan x = sin ² (x/2) •tan x - cot x = - 2cot 2x •sin ² (x/2) = (sin x tan x/2 )/2 = sin²(x/2) •sin²x = [ 2cos ² (x/2) ] [ 1 − cos x ] = sin ²x •(2sin x - sin 2x)/(2sin x + sin 2x ) = tan² (x/2) 2

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 21E
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Bullet 3 - 5 only =))

SUM AND DIFFERENCE, DOUBLE ANGLE, HALF ANGLE IDENTITIES Direction: Verify the following identities •sin ² (x/2) = ( tan x 2 sin x)/ 2tan x •tan x - cot x = - 2cot 2x •sin ² (x/2) = (sin x tan x/2 )/ 2 = sin ² (x/2) sin ²x = [ 2cos ² (x/2) ] [ 1 - cos x ] = sin 2x •(2sin x - sin 2x)/(2sin x + sin 2x ) = tan² (x/2) - sin ² (x/2) 2
Transcribed Image Text:SUM AND DIFFERENCE, DOUBLE ANGLE, HALF ANGLE IDENTITIES Direction: Verify the following identities •sin ² (x/2) = ( tan x 2 sin x)/ 2tan x •tan x - cot x = - 2cot 2x •sin ² (x/2) = (sin x tan x/2 )/ 2 = sin ² (x/2) sin ²x = [ 2cos ² (x/2) ] [ 1 - cos x ] = sin 2x •(2sin x - sin 2x)/(2sin x + sin 2x ) = tan² (x/2) - sin ² (x/2) 2
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