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maths trig test grade 12

Module by: Priscilla Brijlal. E-mail the author

MATHEMATICS GRADE 12

TRIGONOMETRY TEST [25]

QUESTION 1

Simplify without a calculator

tan223otan(−137°)−sin(x−90°)sin(x−360°).sin(90°−x)tan223otan(−137°)−sin(x−90°)sin(x−360°).sin(90°−x)tan223^{o}tan(-137°) - sin(x-90°)sin(x-360°) . sin(90° - x) ( 5 marks )

QUESTION 2

Express Sin 2x and Cos 2x in terms of Sin x and Cos x (2 marks)

QUESTION 3

Simplify without a calculator

cos(360°−x)+2sin(210°−x)cos(360°−x)+2sin(210°−x)Cos (360 ° - x) + 2 Sin (210° - x) (6 marks)

QUESTION 4

Prove the following identity

(Sin2x−cos2x)−1sinx−cosx=2cosx(Sin2x−cos2x)−1sinx−cosx=2cosx{{(Sin2x -Cos 2x)} - 1} over {Sin x -Cos x} = 2 Cos x (6 marks)

QUESTION 6

Determine the GENERAL SOLUTION of the following equation

Cos.sin(3x+10°)+cos(3x+10°).sinx=0,5Cos.sin(3x+10°)+cos(3x+10°).sinx=0,5Cos. Sin (3x + 10° ) + Cos (3x + 10° ) . Sin x = 0,5 (6 marks)

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