Trigonometric Identities
Math ⇒ Trigonometry
Trigonometric Identities starts at 10 and continues till grade 12.
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See sample questions for grade 12
Express sin(3x) in terms of sin(x) only.
Prove that (1 - cos2x)/2 = sin²x.
Prove that 1 + tan²x = sec²x.
Prove that sin(x)sec(x) = tan(x).
If cosθ = 0.6 and θ is in the fourth quadrant, what is sinθ?
If sinθ = 3/5 and θ is in the first quadrant, find cosθ.
If sinA = 0.6 and cosA = 0.8, find tanA.
If sinx = 0.8 and x is in the second quadrant, what is cosx?
Which of the following is a Pythagorean identity?
(1) sin²θ + cos²θ = 1
(2) tan²θ + 1 = sec²θ
(3) 1 + cot²θ = csc²θ
(4) All of the above
Which of the following is equivalent to tan(x) in terms of sin(x) and cos(x)?
(1) sin(x)/cos(x)
(2) cos(x)/sin(x)
(3) 1/sin(x)
(4) 1/cos(x)
Which of the following is NOT a trigonometric identity?
(1) sin²x + cos²x = 1
(2) tanx = sinx/cosx
(3) sinx + cosx = 1
(4) 1 + tan²x = sec²x
Which of the following is the correct double angle formula for cosine?
(1) cos(2x) = 2cos²x - 1
(2) cos(2x) = 1 - 2sin²x
(3) cos(2x) = cos²x - sin²x
(4) All of the above
Fill in the blank: 1 + cot²x = ________.
Fill in the blank: cos(2x) = ________ - 2sin²x.
Fill in the blank: cos(x) = ________ / sec(x).
Fill in the blank: cos²x = (1 + ________)/2.
True or False: tan(A + B) = (tanA + tanB)/(1 - tanA tanB).
True or False: The identity cos(A - B) = cosA cosB + sinA sinB is correct.
True or False: The identity sec²x - tan²x = 1 is valid for all x where secx and tanx are defined.
True or False: The identity sin(2x) = 2sin(x)cos(x) holds for all real values of x.
