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A2.A.67: Simplifying Trigonometric Expressions: Justify the Pythagorean identities
6 If sinA  k , then the value of the expression
(sinA) (cos A) (tanA ) is equivalent to
1) 1
1
2)
k
3) k
4) k 2
1 Which expression always equals 1?
1) cos 2 x  sin 2 x
2) cos 2 x  sin 2 x
3) cos x  sin x
4) cos x  sin x
2 Which equation is not true?
1) cot 2   1  sec 2 
2) sin 2   1  cos 2 
3) sec 2   tan 2   1
4) csc 2   1  cot 2 
7 The expression
1)
2)
3)
3 The expression sin x  cos x  b is equivalent to
1) 1
2) b 2
3) (1  b)(1  b)
4) sinx cos x  b
2
2
2
4)
sin A
cos A
sinA cos A
1
sinA cos A
cos A
sin A
8 The expression
1)
2)
3)
4)
1  cos 2 x
4 The expression
is equivalent to
sin 2 x
1) 1
2) 1
3) sin x
4) cos x
sin 2 A
is equivalent to
tan A
sinx  cos x
is equivalent to
tanx
1
sin 2 x
cos x
cos 2 x
9 Express in simplest terms:
5 The expression cos 2 4  sin 2 4 is equivalent to
1) 1
2) 2
3) cos 
4) cos 8
1
2  2sin 2 x
cos x
ID: A
A2.A.67: Simplifying Trigonometric Expressions: Justify the Pythagorean identities
Answer Section
1 ANS: 2
2 ANS: 1
cot 2   1  sec 2 
REF: 011208a2
cos 2 
1
 1
2
sin 
cos 2 
cos 2  cos 2   1

cos 2 
sin2 
cos 2 
sin 2 

sin2 
cos 2 
REF: 061626a2
3 ANS: 3
4 ANS: 1
REF: 060121siii
REF: 060610b
5 ANS: 1
cos 2 (4)  sin 2 (4)  1
6
7
8
9
REF:
ANS:
ANS:
ANS:
ANS:
060812b
4
2
4
REF: 019026siii
REF: 089023siii
REF: 080032siii
2 cos x.
.
REF: 080526b
1