Question

if (1+ tan 1) (1+tan 2) ......(1+tan45) =2^n the n=?​

Answer 1

Answer:

Step-by-step explanation:

In (1+tan1°) (1+ tan2°) (1+ tan3°) … (1+ tan 45°) =2^n, what does n equal?

First we have to know one conditional identity and that is all.

If A+B=45∘

Then

(1+tanA)(1+tanB)=2

Solution:

=(1+tan1∘)(1+tan2∘)(1+tan3∘)…(1+tan45∘)

= (1+tan1∘)(1+tan44∘)(1+tan2∘)(1+tan43∘)…(1+tan45∘)

Clearly there are 22 pairs of form (1+tanA)(1+tanB)

So, Total =222×2=223

So, n=23