31. show that cos2A = 1-tan² A 1+tan²A
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
Solve all Q31 explaining detailly each step
Transcribed Image Text:26. i) Express: 5cos0- 12sin0 in the form: Reos(0 + a) giving the values of R>0 and a to the
3
nearest degree. Hence find the maximum and minimum values of-
Scose-12sin@|+2
sin30+sine
2tane
27. i) Show that
cos30+cose
1-tan?e
ii) Prove that: sin(sin 0 - cos e) = 20 -1 for 0 <0 s
28. Find the general solution of the equation cos2x + 1 = cosx(.
%3D
sina+sinß
29 i) Prove that
cot()
cosa-cosß
2.
ii) find in radians, the general solution of the equation: tan2x tanx = -1
30. (i) Find the general solution of the equation Cose + 2 sin 0 = 0
(i) Express f(x), where f(x) = cosx + sinx, in the form R cos(x-2). where R>0 and . is an
acute angle. Hence, find the value of x for which the minimum value of
1.
occurs.
f(x)
31. show that cos2A
1-tan A
1+tan²A
Find, in radians, the general solution of the equation cos2x + = sin2x.
i) Find the general solution of the equation: sin 20 = sin@.
i) f(x) = cos x+ 2sin x.
a) Fxpress f(x) in the form: rcos(x-x), where r >0 and 0<x < 90°.
b) Find to the nearest tenth of a degree, the set of values of x which satisfy the equation:
cos x+ 2sin x = 1.
e) Show that: -V5 s cosx + 2 sin x5.
3 i) Given that: f(x)= v3 cosx + sin x, express f(x) in the forım: Rcos (x-2). Where R >
Oand 0 <1<. Hence find the general solution of the equation: f(x) = 3
!!
sin 2x+sin 4x
ii) Prove that:
= tan 2x. Hence find the general solution of the equation:
1+cos 2x+cos 1x
1+cos 2x+cos 4x
=D 0.
sin 2x+sin 1x
34 Express cosx+ V3 sin x in the form R cos (x -A), where R> 0 and 0 <2 <
Hence find
(a) The general solution of the equation cosx + V3 sin x = V3
(b) The maximum and mininium values of cosx + V3 sin x + 2(
95. (i) show that:
sin 0+sin 20
= tan 0
1+cos 0+cos 20
(ii)Find the general solution of the equation sin 4x + cos 2x = 0
%3D
(iiSolve for x ,where0" <x the equation sin 3x + cos x 0
41
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