If A - B -45- find tan A -tan BA- TanAtanBB- 1-tan A tan BC- 1-tan AtanBD- TanAtanB-1

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General Term of Binomial Expansion

If A + B =45∘...

Question

If A + B = $45^{\circ}$ , find tanA + tanB

TanAtanB

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1+tanAtanB

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1 - tanAtanB

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TanAtanB-1

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Solution

The correct option is C
1 - tanAtanB

We have A+B = $45^{\circ}$ and we have to find tanA+tanB. In the options we have tanAtanB also. At this point, we should be able to guess that we are going to use tan (A+B)
Tan (A+B) = tan45 = 1 = $\frac{t a n A + t a n B}{1 - t a n A + t a n B}$
$\Rightarrow$ tanA + tanB = 1 - tanAtanB

Key steps/concepts: (1) Expansion of tan(A+B)

(2) Guessing that the terms in options and question are related to tan (A+B).

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If A + B = 45∘, find tanA + tanB

If A + B = $45^{\circ}$ , find tanA + tanB