Advertisements
Advertisements
Question
Express `tan^-1 ((cos x - sin x)/(cos x + sin x))`, 0 < x < π in the simplest form.
Solution
Consider `((cos x - sin x)/(cos x + sin x))`
Dividing the numerator and denominator by cos x.
we get `(((cosx)/(cosx) - (sin x)/(cosx))/((cos x)/(cos x) + (sin x)/(cosx)))`
`= (1 - tan x)/(1 + tan x)`
`= (tan pi/4 - tan x)/(1 + tan pi/4 tan x)`
`[because tan pi/4 = 1]`
`= tan (pi/4 - x) [because tan ("A - B") = (tan "A" - tan "B")/(1 + tan "A" tan "B")]`
`therefore tan^-1 [tan (pi/4 - x)]`
`= pi/4 - x`
which is the simplest form.
APPEARS IN
RELATED QUESTIONS
Find the value of the following:
If sin−1 x = y, then
Find the domain of the following function:
`f(x)=sin^-1x+sin^-1 2x`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of sin `(A/2)`.
If `sin(sin^-1(1/5) + cos^-1(x))` = 1, then x = ______
Prove that `2 tan^-1 (1/8) + tan^-1 (1/7) + 2tan^-1 (1/5) = pi/4`
Solve: tan-1 (x + 1) + tan-1 (x – 1) = `tan^-1 (4/7)`
Solve the following equation `cos(tan^-1x) = sin(cot^-1 3/4)`
The value of `"cos"^-1 ("cos" ((33 pi)/5))` is ____________.
If 2 tan–1 (cosx) = tan–1 (2 cosec x), then sin x + cos x is equal to ______.
`(tan^-1 (sqrt(3)) - sec^-1(-2))/("cosec"^-1(-sqrt(2)) + cos^-1(-1/2))` is equal to ______.
