-2 -5 is the principal value of

The correct option is A cos^ 1(cos7π/5 )=cos^ 1{cos(2π 3π/5 )} =cos^ 1cos(3π/5 )=3π/5 sin^ 1(sin7π/5 )=sin^ 1{sin(π+2π/5 )} =sin^ 1{ sin2π/5}=sin^ 1{sin( 2π/5 ...

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Standard XII

Mathematics

Trigonometric Ratios for Sum of Two Angles

-2 π/5 is the...

Question

$- \frac{2 π}{5}$ is the principal value of

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Solution

The correct option is B

$c o s^{- 1} (c o s \frac{7 π}{5}) = c o s^{- 1} {c o s (2 π - \frac{3 π}{5})}$
$= c o s^{- 1} c o s (\frac{3 π}{5}) = \frac{3 π}{5}$
$s i n^{- 1} (s i n \frac{7 π}{5}) = s i n^{- 1} {s i n (π + \frac{2 π}{5})}$
$= s i n^{- 1} {- s i n \frac{2 π}{5}} = s i n^{- 1} {s i n (- \frac{2 π}{5})} = - \frac{2 π}{5}$
$s e c^{- 1} (s e c \frac{7 π}{5}) = s e c^{- 1} {s e c (2 π - \frac{3 π}{5})}$
$= s e c^{- 1} (s e c \frac{3 π}{5}) = \frac{3 π}{5}$

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−2π5 is the principal value of

The correct option is B cos−1(cos7π5)=cos−1{cos(2π−3π5)} =cos−1cos(3π5)=3π5 sin−1(sin7π5)=sin−1{sin(π+2π5)} =sin−1{−sin2π5}=sin−1{sin(−2π5)}=−2π5 sec−1(sec7π5)=sec−1{sec(2π−3π5)} =sec−1(sec3π5)=3π5

$- \frac{2 π}{5}$ is the principal value of