The value of sin-1sin 10-1 -2-cos-1cos-5 is

We know, sin^ 1(sin x)=3π x,5π2≤ x≤7π2, ^ 1( x)=x+π, π lt;x lt;0, cos^ 1(cos x)=x+2π, 2π≤ x≤ π ⇒sin^ 1(sin 10)+^ 1( ( 2))+cos^ 1(cos( 5)) =3π 10+( 2+π)+( 5 ...

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Standard XII

Mathematics

Solving Simultaneous Trigonometric Equations

The value of ...

Question

The value of ${sin}^{- 1} (sin 10) + {cot}^{- 1} (cot (- 2)) + {cos}^{- 1} (cos (- 5))$ is

3

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π - 5

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3 π - 13

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6 π - 17

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Solution

The correct option is D $6 π - 17$
We know, ${sin}^{- 1} (sin x) = 3 π - x, \frac{5 π}{2} \leq x \leq \frac{7 π}{2}$ ,
${cot}^{- 1} (cot x) = x + π, - π < x < 0$ ,
${cos}^{- 1} (cos x) = x + 2 π, - 2 π \leq x \leq - π$
$\Rightarrow {sin}^{- 1} (sin 10) + {cot}^{- 1} (cot (- 2)) + {cos}^{- 1} (cos (- 5))$
$= 3 π - 10 + (- 2 + π) + (- 5 + 2 π)$
$= 6 π - 17$

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Solving Simultaneous Trigonometric Equations

Standard XII Mathematics

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The value of sin−1(sin10)+cot−1(cot(−2))+cos−1(cos(−5)) is

The correct option is D 6π−17We know, sin−1(sinx)=3π−x,5π2≤x≤7π2, cot−1(cotx)=x+π,−π<x<0, cos−1(cosx)=x+2π,−2π≤x≤−π ⇒sin−1(sin10)+cot−1(cot(−2))+cos−1(cos(−5)) =3π−10+(−2+π)+(−5+2π) =6π−17

The value of ${sin}^{- 1} (sin 10) + {cot}^{- 1} (cot (- 2)) + {cos}^{- 1} (cos (- 5))$ is