If the area enclosed by the curves - f-x- cos-1-cos x- and - g-x- sin-1-cos x- in - x-9-4-15-4- is - a-2b- -where - a- and - b- are coprime - then the value of - -a-b- is

Side AB=√(( 9π #160; 4 3π) ^ 2 +(π #160; 4 π) ^ 2 ) =√(( 3π #160; 4 ) ^ 2 +( 3π #160; 4 ) ^ 2 ) =√( 2 ) 3π #160; 4 Side BC=√(( ...

You visited us 66 times! Enjoying our articles? Unlock Full Access!

Graphs of Basic Inverse Trigonometric Functions

If the area e...

Question

If the area enclosed by the curves $f (x) = {cos}^{- 1} (cos x)$ and $g (x) = {sin}^{- 1} (cos x)$ in $x \in [\frac{9 π}{4}, \frac{15 π}{4}]$ is $\frac{a π^{2}}{b}$ (where $a$ and $b$ are coprime ), then the value of $(a - b)$ is

Open in App

Solution

Suggest Corrections

Similar questions

L e t f (x) = {s i n}^{- 1} (s i n x) + {c o s}^{- 1} (c o s x), g (x) = m x a n d h (x) = x

π

π

E = {({sin}^{- 1} x)}^{2} + 2 π {cos}^{- 1} x + π^{2}

\frac{a π^{2}}{b},

a

b

(a - b)

L e t f (x) = {s i n}^{- 1} s i n x + {c o s}^{- 1} c o s x,

g (x) = m x a n d h (x) = x

g (x)

f (x), x = π

y = 0

y = ({cot}^{- 1} x) ({cot}^{- 1} (- x))

y

(0, \frac{a π^{2}}{b}]

a, b

a + b

x

sin 3 x (sin 3 x - cos x) = sin x (sin x - cos 3 x)

x \in [0, 2 π]

\frac{a π}{b}

a

b

(a + b)

Join BYJU'S Learning Program