Question

- Tan 6: Tan 42 - Tan66: Tan 78=111
10. If tanu+tan(x+ I) Jan (+ 2/7 ) = 3 then show that tan 3x4​

Answer 1

Answer:

1

Step-by-step explanation:

tan6°tan42°tan66°tan78°

⇒tan(A+B)=1−tanAtanBtanA+tanB

⇒tan(A−B)=1+tanAtanBtanA−tanB

∴tan(A+B).tan(A−B)=1−tan2Atan2Btan2A−tan2B

Let A=60°, then

⇒tan(60°−B)tan(60°+B)=1−tan260°tan2B(tan60°)2−tan2B

                                                          =1−3tan2B3−tan2B

                                                          =tanBtanB.1−3tan2B3−tan2B

                                                          =tan