Question

tan (A + B)= m, tan ( A - B) = n then find cot 2B
​

Answer 1

Answer:

1 + mn / m - n

Step-by-step explanation:

Given--->

tan( A + B ) = m , tan ( A - B ) = n

To find--->

Value of Cot 2B

Solution--->

2 B = B + B

= A + B - A + B

2 B = ( A + B ) - ( A - B )

Taking tan both sides

tan 2 B = tan { (A + B ) - ( A - B ) }

tan ( A + B ) - tan ( A - B ) = ---------------------------------------

1 + tan (A + B ) tan ( A - B )

m - n

tan 2B = --------------

1 + m n

We know that

Cot θ = 1 / tanθ

So

Cot 2B = 1 / tan2B

Cot 2B = (1 + mn ) / ( m - n)

Additional information--->

1)Sin (A + B ) = SinA CosB + CosA SinB

2)Sin (A - B ) = SinA CosB - CosA SinB

3)Cos (A + B) = CosA CosB - SinA SinB

4)Cos (A - B ) = CosA CosB + SinA SinB