Question

Simplify (2/tanA)+(4/tanB)?
Please gave me a solution of this question.

Answer 1

We will prove tanA +tanB using equation tan(a+b).

First, you need to write this expression correctly, using brackets:

tan(a+b) = (tan a + tan b)/(1 - tan a*tan b)

We'll prove this identity, using the fact that tangent function is a ratio of :

tan (a+b) = sin (a+b)/cos (a+b)

We'll use the following identities:—

# sin (a+b) = sin a*cos b + sin b*cos a

# cos (a+b) = cos a*cos b - sin a*sin b

tan (a+b) = (sin a*cos b + sin b*cos a)/(cos a*cos b - sin a*sin b)

We'll force factor cos a*cos b, both numerator and denominator, creating the tangent functions within brackets:

tan (a+b) = cos a*cos b( tan a + tan b)/cos a*cos b(1 - tan a*tan b)

We'll simplify and now you get:

tan (a+b) = (tan a + tan b)/(1 - tan a*tan b)

Now rearranging;

Formula of tan (A+B) =

tanA+ tanB =tan(a+b) ×(1-tanA×tanB)

Or

We know that ;-

tanA+ tanB = sinA/cosA + sinB/cosB

=( sinAcosB+sinBcosA) /cosAcosB

=sin(A+B) /cosAcosB

Therefore;-

tanA+ tanB =sin(A+B)/cosAcosB

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