Cos -1cos7 -6 is equal toa 7 -6b 5 -6-6c 5 -6d

Cos^ 1 ( cos7π/6 )=cos^ 1 [cos ( 2π 5π/6 ) ] where, 5π/6ϵ [0,π] ∴ cos^ 1 ( cos7π/6 )=cos^ 1 [ cos ( 5π/6 ) ]=5π/6 [∵ cos(2π θ)=cosθ] Hence, the correc ...

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Standard XII

Mathematics

Greatest Integer Function

cos -1cos7 π/...

Question

$c o s^{- 1} (c o s \frac{7 π}{6})$ is equal to
a) $\frac{7 π}{6}$
b) $\frac{5 π}{6}$
c) $\frac{π}{3}$
d) $\frac{π}{6}$

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Solution

$c o s^{- 1} (c o s \frac{7 π}{6}) = c o s^{- 1} [c o s (2 π - \frac{5 π}{6})]$
where, $\frac{5 π}{6} ϵ [0, π] ∴ c o s^{- 1} (c o s \frac{7 π}{6}) = c o s^{- 1} [c o s (\frac{5 π}{6})] = \frac{5 π}{6}$
$[∵ c o s (2 π - θ) = c o s θ]$

Hence, the correct options is (b).

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cos−1(cos7π6) is equal to a) 7π6 b) 5π6 c) π3 d) π6

cos−1(cos7π6)=cos−1[cos(2π−5π6)] where, 5π6ϵ[0,π] ∴ cos−1(cos7π6)=cos−1[cos(5π6)]=5π6 [∵cos(2π−θ)=cosθ] Hence, the correct options is (b).

$c o s^{- 1} (c o s \frac{7 π}{6})$ is equal to
a) $\frac{7 π}{6}$
b) $\frac{5 π}{6}$
c) $\frac{π}{3}$
d) $\frac{π}{6}$

$c o s^{- 1} (c o s \frac{7 π}{6}) = c o s^{- 1} [c o s (2 π - \frac{5 π}{6})]$
where, $\frac{5 π}{6} ϵ [0, π] ∴ c o s^{- 1} (c o s \frac{7 π}{6}) = c o s^{- 1} [c o s (\frac{5 π}{6})] = \frac{5 π}{6}$
$[∵ c o s (2 π - θ) = c o s θ]$

Hence, the correct options is (b).