If A + B + C = π , cos B = cos A   cos C , then tan A   tan C =

If A+B+C=π,cosB=cosA cosC, then tanA tanC=
  1. 0
  2. 1
  3. 2
  4. 12

Solution

Given, 

A+B+C=π

Now,

cosB=cosAcosC

⇒cosπ-A+C=cosAcosC

⇒-cosA+C=cosAcosC

⇒cosAcosC-sinAsinC=-cosAcosC

⇒sinAsinC=2cosAcosC

⇒tanAtanC=2.

Asked in: AP EAMCET 2022 (04 Jul Shift 2)

Practice more Trigonometric Equations questions on Aicharya