The value of sin -1-cos33 -5- isa 3 -5b -7 -5c -10d -10

(d) We have, sin^ 1(cos33π/5 )=sin^ 1[cos(6π+3π/5 ) ]=sin^ 1[cos(3π/5 ) ] [∵ cos(2nπ + θ)=cos θ ] =sin^ 1 [ cos(π/2+π/10 ) ]=sin^ 1( sinπ/10 ) = sin^ ...

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Byju's Answer

Standard XII

Mathematics

De-Moivre's Theorem

The value of ...

Question

The value of $s i n^{- 1} [c o s (\frac{33 π}{5})]$ is

(a) $\frac{3 π}{5}$ (b) $\frac{- 7 π}{5}$ (c) $\frac{π}{10}$ (d) $\frac{- π}{10}$

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Solution

(d) We have,

$s i n^{- 1} (c o s \frac{33 π}{5}) = s i n^{- 1} [c o s (6 π + \frac{3 π}{5})] = s i n^{- 1} [c o s (\frac{3 π}{5})] [∵ c o s (2 n π + θ) = c o s θ] = s i n^{- 1} [c o s (\frac{π}{2} + \frac{π}{10})] = s i n^{- 1} (- s i n \frac{π}{10}) = - s i n^{- 1} (s i n \frac{π}{10}) [∵ s i n^{- 1} (- x) = - s i n^{- 1} x] = - \frac{π}{10} [∵ s i n^{- 1} (s i n x) = x, x \in (\frac{- π}{2}, \frac{π}{2})]$

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Similar questions

The value of $c o s^{- 1} (c o s \frac{3 π}{2})$ is

(a) $\frac{π}{2}$ (b) $\frac{3 π}{2}$ (c) $\frac{5 π}{2}$ (d) $\frac{7 π}{2}$

Q. If a curve is represented parametrically by the equations

x = sin (t + \frac{7 π}{12}) + sin (t - \frac{π}{12}) + sin (t + \frac{3 π}{12})

y = cos (t + \frac{7 π}{12}) + cos (t - \frac{π}{12}) + cos (t + \frac{3 π}{12}),

then the value of

\frac{d}{d t} (\frac{x}{y} - \frac{y}{x})

t = \frac{π}{8}

Q. If a curve is represented parametrically by

x = sin (t + \frac{7 π}{12}) + sin (t - \frac{π}{12}) + sin (t + \frac{3 π}{12}),

y = cos (t + \frac{7 π}{12}) + cos (t - \frac{π}{12}) + cos (t + \frac{3 π}{12})

, then the value of

\frac{d}{d t} (\frac{x}{y} - \frac{y}{x})

t = \frac{π}{8}

Q. If a curve is represented parametrically by

x = sin (t + \frac{7 π}{12}) + sin (t - \frac{π}{12}) + sin (t + \frac{3 π}{12}),

y = cos (t + \frac{7 π}{12}) + cos (t - \frac{π}{12}) + cos (t + \frac{3 π}{12})

, then the value of

\frac{d}{d t} (\frac{x}{y} - \frac{y}{x})

t = \frac{π}{8}

Q. If a curve is represented parametrically by the equations.

x = sin (t + \frac{7 π}{12}) +

sin (t - \frac{π}{12}) + sin (t + \frac{3 π}{12}),

y = cos (t + \frac{7 π}{12}) + cos (t - \frac{π}{12}) + cos (t + \frac{3 π}{12})

then find the value of

\frac{d}{d t} (\frac{x}{y} - \frac{y}{x})

t = \frac{π}{8}

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The value of sin−1[cos(33π5)] is (a) 3π5 (b) −7π5 (c) π10 (d) −π10

(d) We have, sin−1(cos33π5)=sin−1[cos(6π+3π5)]=sin−1[cos(3π5)] [∵ cos(2nπ + θ)=cos θ]=sin−1[cos(π2+π10)]=sin−1(−sinπ10)=−sin−1(sinπ10) [∵ sin−1(−x)=−sin−1 x]=−π10 [∵ sin−1 (sin x)=x, x∈(−π2,π2)]

The value of $s i n^{- 1} [c o s (\frac{33 π}{5})]$ is

(a) $\frac{3 π}{5}$ (b) $\frac{- 7 π}{5}$ (c) $\frac{π}{10}$ (d) $\frac{- π}{10}$