Question

If A+B+C =90 degreesthen Tan2A+Tan2B+Tan2C =
2) Cot2A Cot2B Cot2C
1) Sin2A Sin2B Sin2C
3) Cos2A Cos2B Cos2C
4) Tan2A Tan2B Tan2C​

Answer 1

Two diameters AB and CD intersect each other at O. AC, CB and BD are joined

∠DBA = 50°

∠DBA and ∠DCA are in the same segment

∴ ∠DBA = ∠DCA = 50°

In ∆OAC, OA = OC (Radii of the circle)

∴ ∠OAC = ∠OCA = ∠DCA = 50°

and ∠OAC + ∠OCA + ∠AOC = 180° (Sum of angles of a triangle)

⇒ 50° + 50° + ∠AOC = 180°

⇒ 100° + ∠AOC = 180°

⇒ ∠AOC = 180° – 100° = 80°

Hence ∠AOC = 80°