Multiple choice

If ( \cot (P+Q) = 0 ) and ( \tan (P-Q) = \frac{1}{\sqrt{3}} ), then what is the value of ( \angle P ) and ( \angle Q )? ( (0^{\circ} < P, Q \le 90^{\circ}) )

  1. 25 degree, 65 degree

  2. 45 degree, 45 degree

  3. 60 degree, 30 degree

  4. 15 degree, 75 degree
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From cot(P+Q) = 0, we get P+Q = 90 degrees. From tan(P-Q) = 1/sqrt(3), we get P-Q = 30 degrees. Solving these equations: P = (90+30)/2 = 60 degrees, Q = (90-30)/2 = 30 degrees.

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