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If (sin x + cos x)/ (sin x – cos x) = (9 + √11)/(9 - √11), find the value of tan x.
- A0
- B1
- C-1
- DNone of these
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CCommunity
(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.
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.