Question

if tanQ + cotQ=2 prove Q=45 degree using quadratic equations tan45 degree=1 cot45 degree=1

Answer 1

cotQ = 1/tanQ, so we can rewrite tanQ + 1/tanQ = 2.

Replace tanQ with t, we get t + 1/t = 2.

Now we can solve a quadratic equation.

→ t² + 1 = 2t → t² - 2t + 1 = 0 → t = 1 (double root)

Therefore tanQ = 1 and so is cotQ = 1.