Let fx-ecos -1sinx-3-then

The correct options are B f ( 8π/9 )= e^13π/18 C f ( 7π/4 )= e^π/12 f(x)=e^cos^ 1 ( cos (π/2 x π/3 ) )=e^cos^ 1 (cos (π/6 x ) ) ∴ f ( 8π/9 )= e^cos^ ...

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Byju's Answer

Standard XII

Mathematics

General Solution of Trigonometric Equation

Let fx=ecos -...

Question

Let $f (x) = e^{c o s^{- 1} s i n (x + \frac{π}{3})}$ ,then

$f (\frac{8 π}{9}) = e^{\frac{5 π}{18}}$

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$f (\frac{8 π}{9}) = e^{\frac{13 π}{18}}$

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$f (- \frac{7 π}{4}) = e^{\frac{π}{12}}$

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$f (\frac{7 π}{4}) = e^{\frac{11 π}{12}}$

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Solution

The correct options are
B
$f (\frac{8 π}{9}) = e^{\frac{13 π}{18}}$

C
$f (- \frac{7 π}{4}) = e^{\frac{π}{12}}$

$f (x) = e^{c o s^{- 1}} (c o s (\frac{π}{2} - x - \frac{π}{3})) = e^{c o s^{- 1} (c o s (\frac{π}{6} - x))}$

$∴ f (\frac{8 π}{9}) = e^{c o s^{- 1} (c o s (\frac{π}{6} - \frac{8 π}{9}))} = e^{c o s^{- 1} (c o s (- \frac{13 π}{18}))}$ $= e^{c o s^{- 1} (c o s (\frac{13 π}{18}))} = \frac{13 π}{18};$ Similarly find $f (- \frac{7 π}{4})$

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Let f(x)=ecos−1sin(x+π3),then

The correct options are B f(8π9)=e13π18 C f(−7π4)=eπ12 f(x)=ecos−1(cos(π2−x−π3))=ecos−1(cos(π6−x)) ∴f(8π9)=ecos−1(cos(π6−8π9))=ecos−1(cos(−13π18)) =ecos−1(cos(13π18))=13π18; Similarly find f(−7π4)

Let $f (x) = e^{c o s^{- 1} s i n (x + \frac{π}{3})}$ ,then