Evaluate- - 1 x - 1x - 1 - sin - 1 x - 2x - 1

Solution : sec^ 1(x+1/x 1)+sin^ 1(x 1/x+1) ⇒ cos^ 1(x 1/x+1)+sin^ 1(x 1/x+1) ⇒π/2 ...

121

You visited us 121 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Basic Inverse Trigonometric Functions

Evaluate: -...

Question

Evaluate: ${sec}^{- 1} (\frac{x + 1}{x - 1}) + {sin}^{- 1} (\frac{x - 2}{x + 1})$

Open in App

Solution

Solution :-

$s e c^{- 1} (\frac{x + 1}{x - 1}) + s i n^{- 1} (\frac{x - 1}{x + 1})$

$\Rightarrow c o s^{- 1} (\frac{x - 1}{x + 1}) + s i n^{- 1} (\frac{x - 1}{x + 1})$

$\Rightarrow \frac{π}{2}$

Suggest Corrections

Similar questions

Q. Evaluate:

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

x = \frac{1}{5}

Q. Evaluate :

\int_{0}^{1} {sin}^{- 1} (x \sqrt{1 - x} - \sqrt{x} \sqrt{1 - x^{2}}) d x, 0 \leq x \leq 1

Q. Evaluate:

lim x \to \frac{1}{\sqrt{2}}

\frac{x - cos ({sin}^{- 1} x)}{1 - tan ({sin}^{- 1} x)}

Q. Evaluate:

∣ ∣ ∣ \begin{matrix} x^{2} - x + 1 & x - 1 x + 1 & x + 1 \end{matrix} ∣ ∣ ∣

Inverse circular functions,Principal values of ${sin}^{- 1} x, {c o s}^{- 1} x, {tan}^{- 1} x$ .
${tan}^{- 1} x + {tan}^{- 1} y = {tan}^{- 1} \frac{x + y}{1 - x y}$ , $x y < 1$
$π + {tan}^{- 1} \frac{x + y}{1 - x y}$ , $x y > 1$ .
Evaluate the following :
(a) $sin [\frac{π}{3} - {sin}^{- 1} (- \frac{1}{2})]$
(b) $sin [\frac{π}{2} - {sin}^{- 1} (- \frac{\sqrt{3}}{2})]$

Join BYJU'S Learning Program

Evaluate: sec−1(x+1x−1)+sin−1(x−2x+1)

Solution :-sec−1(x+1x−1)+sin−1(x−1x+1)⇒cos−1(x−1x+1)+sin−1(x−1x+1)⇒π2

Evaluate: ${sec}^{- 1} (\frac{x + 1}{x - 1}) + {sin}^{- 1} (\frac{x - 2}{x + 1})$

Solution :-

$s e c^{- 1} (\frac{x + 1}{x - 1}) + s i n^{- 1} (\frac{x - 1}{x + 1})$

$\Rightarrow c o s^{- 1} (\frac{x - 1}{x + 1}) + s i n^{- 1} (\frac{x - 1}{x + 1})$

$\Rightarrow \frac{π}{2}$