Trigonometric Identities
Math ⇒ Trigonometry
Trigonometric Identities starts at 10 and continues till grade 12.
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Prove that 1 – sin²θ = cos²θ.
Prove that sin(π – θ) = sinθ.
Prove that tan(–θ) = –tanθ.
State the co-function identity for sin(90° - θ).
Which of the following is equivalent to 1 + tan²θ?
(1) sec²θ
(2) csc²θ
(3) sin²θ
(4) cos²θ
Which of the following is the correct expression for cos(α + β)?
(1) cosα cosβ – sinα sinβ
(2) cosα cosβ + sinα sinβ
(3) cosα + cosβ
(4) sinα + sinβ
Which of the following is the correct expression for sin²θ in terms of cos²θ?
(1) 1 – cos²θ
(2) 1 + cos²θ
(3) cos²θ – 1
(4) 2cos²θ
Which of the following is the correct half-angle identity for sin²(θ/2)?
(1) (1 – cosθ)/2
(2) (1 + cosθ)/2
(3) (1 – sinθ)/2
(4) (1 + sinθ)/2
Which of the following is the correct identity for cos²θ in terms of sin²θ?
(1) 1 – sin²θ
(2) 1 + sin²θ
(3) sin²θ – 1
(4) 2sin²θ
Which of the following is the correct identity for sin(α – β)?
(1) sinα cosβ – cosα sinβ
(2) sinα sinβ + cosα cosβ
(3) sinα cosβ + cosα sinβ
(4) sinα – sinβ
Which of the following is the correct Pythagorean identity?
(1) sin²θ + cos²θ = 1
(2) sin²θ - cos²θ = 1
(3) sinθ + cosθ = 1
(4) sinθ - cosθ = 1
Which of the following is the double angle identity for sin2θ?
(1) 2sinθcosθ
(2) sin²θ - cos²θ
(3) 2tanθ
(4) 2sin²θ
Fill in the blank: cos(2θ) = 2cos²θ – ________.
Fill in the blank: cos(90° – θ) = ________.
Fill in the blank: csc²θ – cot²θ = ________.
Fill in the blank: secθ is the reciprocal of ________.
True or False: cos(–θ) = cosθ for all θ.
True or False: cotθ = 1/tanθ for all θ where tanθ ≠ 0.
True or False: sec²θ – tan²θ = 1 for all θ where secθ and tanθ are defined.
True or False: tanθ = sinθ / cosθ for all values of θ where cosθ ≠ 0.
