Express as a single trigonometric function. (a) cos 2a cos a (c) sin 5 cos 2 (d) sin 2mm - cos 5 sin 2 sin 2a sin a (b) cos x cos 4x + sin x sin 4x

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 40E
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A 1. Express as a single trigonometric function.
(a) cos 2a cos a sin 2a sin a (b) cos x cos 4x + sin x sin 4x
(c) sin 5 cos 2- cos 5 sin 2
(d) sin 2m cos m + cos 2m sin m
tan 2a + tan 3a
(e)
(g)
(i)
1-tan 2a tan 3a
cos² x sin² x
tan x + tan x
1- tan² x
2. Evaluate using formulas developed in this section.
13-2
B (a) sin
(b) cos
12
5. If x is in the interval
12
اکار
(e) sin 75°
3. Find the value of each of the following.
(a) sin(-)
cos x = -and tan y =
(a) sin(x + y)
(b)
a sin
4. If x and y are in the interval (0.7) and sinx=and cos y =
evaluate each of the following.
(a) sin(x - y)
(f)
(h)
()
- sin
(c) cos[
(b) cos(x + y)
TT
Use the identity tan =
(e) cos
(g) sin(x
cos(-7-7)(c)
6. Find the exact value of each of the following.
(a) sin 50° cos 20°
cos 50° sin 20°
म 4T
(b) cos Cos
4T
21
21
tan 7° + tan 8°
1 tan 7° tan 8°
STT
5T
COS
36 18
tan 7-tan 9
1+tan 7 tan 9
sin a cos ca+ cos a sin a
cos¹ 2+ sin² 2
(d) tan(-2)
(f) cos(-15°)
sin
and y is in the interval
, evaluate each of the following.
cos(x - y) (c) tan(x - y)
+ cos sin
5T
5T
36 18
Use the Addition Formula for Sine to prove the Subtraction Formula
for Sine, namely, sin(a - b) = sin a cos b- cos a sin b.
sin e
10. Prove each of the following.
(a) sin(+ x) = -sin x
13T
2
+ x) = sin x
cos e
Tangent, namely tan(a - b) =
(c) tan(x + y)
+ x) = -sin x
TT) = -sin x
Use the Addition Formula for Tangent to prove the Subtraction
Formula for Tangent.
to prove the Subtraction Formula for
tan a tan b
1+tan a tan b
and
(b) tan(2-x) = -tan x
/3TT
(d) sin
T
+
=-COS X
(f) tan
(h) -tan(-x- π) = tan x
=-cot x
Transcribed Image Text:A 1. Express as a single trigonometric function. (a) cos 2a cos a sin 2a sin a (b) cos x cos 4x + sin x sin 4x (c) sin 5 cos 2- cos 5 sin 2 (d) sin 2m cos m + cos 2m sin m tan 2a + tan 3a (e) (g) (i) 1-tan 2a tan 3a cos² x sin² x tan x + tan x 1- tan² x 2. Evaluate using formulas developed in this section. 13-2 B (a) sin (b) cos 12 5. If x is in the interval 12 اکار (e) sin 75° 3. Find the value of each of the following. (a) sin(-) cos x = -and tan y = (a) sin(x + y) (b) a sin 4. If x and y are in the interval (0.7) and sinx=and cos y = evaluate each of the following. (a) sin(x - y) (f) (h) () - sin (c) cos[ (b) cos(x + y) TT Use the identity tan = (e) cos (g) sin(x cos(-7-7)(c) 6. Find the exact value of each of the following. (a) sin 50° cos 20° cos 50° sin 20° म 4T (b) cos Cos 4T 21 21 tan 7° + tan 8° 1 tan 7° tan 8° STT 5T COS 36 18 tan 7-tan 9 1+tan 7 tan 9 sin a cos ca+ cos a sin a cos¹ 2+ sin² 2 (d) tan(-2) (f) cos(-15°) sin and y is in the interval , evaluate each of the following. cos(x - y) (c) tan(x - y) + cos sin 5T 5T 36 18 Use the Addition Formula for Sine to prove the Subtraction Formula for Sine, namely, sin(a - b) = sin a cos b- cos a sin b. sin e 10. Prove each of the following. (a) sin(+ x) = -sin x 13T 2 + x) = sin x cos e Tangent, namely tan(a - b) = (c) tan(x + y) + x) = -sin x TT) = -sin x Use the Addition Formula for Tangent to prove the Subtraction Formula for Tangent. to prove the Subtraction Formula for tan a tan b 1+tan a tan b and (b) tan(2-x) = -tan x /3TT (d) sin T + =-COS X (f) tan (h) -tan(-x- π) = tan x =-cot x
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