Find the value of cos- - 2 - sin -1 1 3 -

cos[π2 sin^ 113]=cos(cos^ 113)=13 Since, #160; sin^ 1x+cos^ 1x=π2, #160;∀ x∈ [ 1,1] ...

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Standard XII

Mathematics

Domain and Range of Basic Inverse Trigonometric Functions

Find the valu...

Question

Find the value of $cos [\frac{π}{2} - {sin}^{- 1} (\frac{1}{3})]$

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Solution

$cos [\frac{π}{2} - {sin}^{- 1} \frac{1}{3}] = cos ({cos}^{- 1} \frac{1}{3}) = \frac{1}{3}$

Since, ${sin}^{- 1} x + {cos}^{- 1} x = \frac{π}{2}, \forall x \in [- 1, 1]$

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Similar questions

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sin [\frac{π}{3} - {sin}^{- 1} (\frac{- 1}{2})]

Q. If

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t = \frac{π}{3} .

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

Q. Find the value of

{cos}^{- 1} (cos \frac{2 π}{3}) + {sin}^{- 1} (sin \frac{2 π}{3})

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Find the value of cos[π2−sin−1(13)]

cos[π2−sin−113]=cos(cos−113)=13Since, sin−1x+cos−1x=π2,∀x∈[−1,1]

Find the value of $cos [\frac{π}{2} - {sin}^{- 1} (\frac{1}{3})]$

$cos [\frac{π}{2} - {sin}^{- 1} \frac{1}{3}] = cos ({cos}^{- 1} \frac{1}{3}) = \frac{1}{3}$

Since, ${sin}^{- 1} x + {cos}^{- 1} x = \frac{π}{2}, \forall x \in [- 1, 1]$