Question:

In a triangle ABC, tan C < 0. Then

Updated On: Apr 27, 2024
  • (A) tan A . tan B < 1
  • (B) tan A . tan B > 1
  • (C) tan A + tan B + tan C < 0
  • (D) tan A + tan B + tan C > 0
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The Correct Option is A, D

Solution and Explanation

Explanation:
Here, tan⁡C<0⇒C is obtuse.⇒A and B are acute and A+B<π2 tan⁡(A+B)=tan⁡A+tan⁡B1−tan⁡Atan⁡B>0⇒1−tan⁡A⋅tan⁡B>0⇒tan⁡Atan⁡B<1tan⁡A+tan⁡B+tan⁡C=(+)(+)(−)<0=tan⁡A⋅tan⁡B⋅tan⁡CinΔABC
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