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Find the values of (cos A - sin A) and (tan A + cot A) for each of the following: (a) A = 2pi/3, (b) A = 7pi/4, (c) A = 11pi/3, (d) A = 5pi/4.

1. (a) -(1+sqrt(3))/2, -4/sqrt(3); (b) sqrt(2), -2; (c) (1-sqrt(3))/2, -4/sqrt(3); (d) 0, 2
2. (a) (1+sqrt(3))/2, 4/sqrt(3); (b) sqrt(2), 2; (c) (1+sqrt(3))/2, 4/sqrt(3); (d) 0, 2
3. (a) -(1+sqrt(3))/2, 4/sqrt(3); (b) -sqrt(2), -2; (c) (1-sqrt(3))/2, 4/sqrt(3); (d) sqrt(2), 2
4. (a) -(1+sqrt(3))/2, -4/sqrt(3); (b) sqrt(2), 2; (c) (1+sqrt(3))/2, -4/sqrt(3); (d) sqrt(2), -2

Correct answer: (a) -(1+sqrt(3))/2, -4/sqrt(3); (b) sqrt(2), -2; (c) (1-sqrt(3))/2, -4/sqrt(3); (d) 0, 2

Solution

Evaluating sine, cosine, tangent and cotangent in the proper quadrant for each angle gives the listed pairs; note 11pi/3 is coterminal with -pi/3.

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