TOPIC 26 | factor formula set 1 of 2 get the full set details at the bottom of page
Question 1:
Express cos 3x + cos x as a product of trigonometric functions.
Question 2:
By using the factor formula, or otherwise, express cos6θ + cos 2θ as a
product of trigonometric functions.
Hence, solve the equation cos 2θ + cos 4θ + cos6θ =
0 , for 0° ≤ θ ≤ 180°
Question 3:
Solve the equation given below for 0° ≤ x ≤ 180° : sin 3x − sin 2x + sin x =
0
Question 4:
cos( A + B) 4
Given that
= , prove that 9 tanA = cotB
cos( A − B) 5
1
and A is obtuse, find without using
Given further that tan( A − B) =
tan A
the calculator the value of tan A
Question 5:
(a) Show that sin x + 3sin 3x + sin
=
5x sin 3x( 4cos 2 x + 1)
(b) Hence solve the equation sin x + 3sin 3x + sin 5x =
4 sin 3x cos x for
0 ≤ x ≤ 120°
Question 6:
1
(sin 2x + sin x) in the form asinbx coscx
2
1
(b) Express (sin 3x − sin 2x) in the form asinbx coscx
2
(a) Express
Question 7:
(a) Express 3cosθ − 5 sinθ in the form Rcos(θ + α ) , where R > 0 and
0 < α < 90° .
Hence, find all the angles between 0 0 and 360 o which satisfy the
equation 3cosθ − 5 sinθ =
2
(b) The curve
=
y acos(bθ ) − c , where a, b and c are positive integers, and
0 ≤ θ ≤ 2π , has an amplitude of 4 and a period of
value of y is 1. State the values of a, b and c.
π
3
. The maximum
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TOPIC 26 | factor formula set 1 of 2 get the full set details at the bottom of page
Question 8:
sin( A + B) 2
tan B
Given that
= , evaluate
sin( A − B) 3
tan A
Question 9:
sin 3A − sin A
Prove
= tan A
cos A + cos 3A
Question 10:
cos9A + cos 4A + cos A
Prove that
≡ cot 4A
sin9A + sin 4A − sin A
Question 11:
sin 2A + sin 4A + sin6A
Prove that
= tan 4A
cos 2A + cos 4A + cos6A
Question 12:
cos( A − B) 3
Given that
= , find the value of tan A × tan B
cos( A + B) 5
Question 13:
Show that sin15° sin75° =
1
4
Question 14:
cos( A + B) 4
Given that
= , find the value of tan Atan B
cos( A − B) 5
Question 15:
(a) Show that sin 3x + sin x =
4 sin x cos 2 x
(b) Hence, find all the angles between 0 and 2π which satisfy the equation
sin 3x − sin x =
0
Question 16:
sin 3θ − sin 3∅
If θ = 45 0 and ∅ =30 0 , find the value of a in surd
Simplify
cos 3θ + cos3∅
sin 3θ − sin 3∅
form if
=a
cos 3θ + cos3∅
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TOPIC 26 | factor formula set 1 of 2 get the full set details at the bottom of page
Question 17:
1
1
If cot ( x + y ) =and cot ( x − y ) =, determine the following expressions in
a
b
terms of a and b:
cos 2x + cos 2y
(a)
cos 2x − cos2y
cos 2x − cos 2y
(b)
sin 2x − sin2y
sin 4x + sin 4y
(c)
sin 4x − sin 4y
sin 2x − sin 2y
(d)
sin 2x + sin2y
Question 18:
sin8x + sin 2x
1
Show that
= 2sin x − cosec x
cos7x − cos 3x
2
Question 19:
Prove that sin 2x cos x − cos 2x sin x =
sin x
Question 20:
1
1
If tan A = and tan B = , find the value of tan ( 2B + A )
8
5
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