If $\sin^{-1}\left(\frac{x}{5}\right)+\operatorname{cosec}^{-1}\left(\frac{5}{4}\right)=\frac{\pi}{2}$ then a value of $x$ is

JEE Main · 2007 · 29 Apr 2007 · Offline · Inverse Trigonometric Functions

sin^{- 1} (\frac{x}{5}) + cosec^{- 1} (\frac{5}{4}) = \frac{π}{2}

then a value of

x

Answer: (B)

Write the cosecant inverse as

cosec^{- 1} \frac{5}{4} = sin^{- 1} \frac{4}{5}

, so the equation becomes

sin^{- 1} \frac{x}{5} + sin^{- 1} \frac{4}{5} = \frac{π}{2}

. That means

sin^{- 1} \frac{x}{5} = \frac{π}{2} - sin^{- 1} \frac{4}{5} = cos^{- 1} \frac{4}{5} = sin^{- 1} \frac{3}{5}

. Hence

\frac{x}{5} = \frac{3}{5}

, giving

x = 3

JEE Main · 2007 · 29 Apr 2007 · Offline · Single correct option

If the domain of the function $f (x) = cos^{- 1} (\frac{2 x - 5}{11 - 3 x}) + sin^{- 1} (2 x^{2} - 3 x + 1)$ is the interval $[α, β]$ , then $α + 2 β$ is equal to :
JEE Main 2026View solution →
The number of solutions of $tan^{- 1} 4 x + tan^{- 1} 6 x = \frac{π}{6}$ , where $- \frac{1}{2 6} < x < \frac{1}{2 6}$ is equal to
JEE Main 2026View solution →
If the domain of the function $f (x) = sin^{- 1} (\frac{1}{x ^{2} - 2 x - 2})$ , is $(- \infty, α] \cup [β, γ] \cup [δ, \infty)$ , then $α + β + γ + δ$ is equal to
JEE Main 2026View solution →
If $k = tan (\frac{π}{4} + \frac{1}{2} cos^{- 1} (\frac{2}{3})) + tan (\frac{1}{2} sin^{- 1} (\frac{2}{3}))$ then the number of solutions of the equation …
JEE Main 2026View solution →
Considering the principal values of inverse trigonometric functions, the value of the expression $tan (2 sin^{- 1} (\frac{2}{13}) - 2 cos^{- 1} (\frac{3}{10}))$ is equal to :
JEE Main 2026View solution →
Let [ • ] denote the greatest integer function. If the domain of the function $f (x) = cos^{- 1} (\frac{4 x + 2 [ x ]}{3})$ is $[α, β]$ , then $12 (α + β)$ is equal to :
JEE Main 2026View solution →