If (sin x + cos x)/ (sin x – cos x) = (9 + √11)/(9

If (sin x + cos x)/ (sin x – cos x) = (9 + √11)/(9 - √11), find the value of tan x.

A 0

B 1

C -1

D 2

E None of these

Correct Answer: Option E

(sin x + cos x)/(sin x – cos x) = (9 + √11)/ (9 - √11)

We know that if (a + b)/(a – b) = (c + d)/(c – d), then a/b = c/d (by componendo and dividendo)

Thus if we compare the given equation we get, a = sin x , b = cos x, c = 9, d = √11

Therefore, sin x/cos x = 9/√11……… (i)

And we know that sin x/cos x = tan x

Putting in (i), we get

tan x = 9/√11

The value of tan x is 9/√11.