Match the following lists:List IList IIa. Let θ=sin−1(sin(−600°)), then value of θ isp. π/5b. sin−11213+cos−145+tan−16316=q. π/3c. If tan−1x+tan−1y=4π5, then cot−1x+cot−1y equalsr. π/4d. tan−117+2tan−113=s. π

sin−1sin(−600×π180)=sin−1sin(−10π3)=sin−1[−sin(4π−2π3)]=sin−1(sin2π3)=sin−1(sin(π−π3))=sin−1(sinπ3)=π3.

Match the following lists:List IList IIa. Let θ=sin−1(sin(−600°)), then value of θ isp. π/5b. sin−11213+cos−145+tan−16316=q. π/3c. If tan−1x+tan−1y=4π5, then cot−1x+cot−1y equalsr. π/4d. tan−117+2tan−113=s. π

sin−1sin(−600×π180)=sin−1sin(−10π3)=sin−1[−sin(4π−2π3)]=sin−1(sin2π3)=sin−1(sin(π−π3))=sin−1(sinπ3)=π3.

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Match the following lists:
List I List II
a. Let $θ = \sin^{- 1} (\sin (- 600 °)),$ then value of $θ$ is p. $π / 5$
b. $\sin^{- 1} \frac{12}{13} + \cos^{- 1} \frac{4}{5} + \tan^{- 1} \frac{63}{16} =$ q. $π / 3$
c. If $\tan^{- 1} x + \tan^{- 1} y = \frac{4 π}{5},$ then $\cot^{- 1} x + \cot^{- 1} y$ equals r. $π / 4$
d. $\tan^{- 1} \frac{1}{7} + 2 \tan^{- 1} \frac{1}{3} =$ s. $π$

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$a - r b - s c - p d - q$

$a - q b - s c - r d - p$

$a - q b - s c - p d - r$

$a - s b - q c - p d - r$

answer is A.

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$\sin^{- 1} \sin (- 600 \times \frac{π}{180}) = \sin^{- 1} \sin (\frac{- 10 π}{3})$

$= \sin^{- 1} [- \sin (4 π - \frac{2 π}{3})] = \sin^{- 1} (\sin \frac{2 π}{3})$

$= \sin^{- 1} (\sin (π - \frac{π}{3})) = \sin^{- 1} (\sin \frac{π}{3}) = \frac{π}{3} .$

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List I	List II
a. Let $θ = \sin^{- 1} (\sin (- 600 °)),$ then value of $θ$ is	p. $π / 5$
b. $\sin^{- 1} \frac{12}{13} + \cos^{- 1} \frac{4}{5} + \tan^{- 1} \frac{63}{16} =$	q. $π / 3$
c. If $\tan^{- 1} x + \tan^{- 1} y = \frac{4 π}{5},$ then $\cot^{- 1} x + \cot^{- 1} y$ equals	r. $π / 4$
d. $\tan^{- 1} \frac{1}{7} + 2 \tan^{- 1} \frac{1}{3} =$	s. $π$

Match the following lists:List IList IIa. Let θ=sin−1(sin(−600°)), then value of θ isp. π/5b. sin−11213+cos−145+tan−16316=q. π/3c. If tan−1x+tan−1y=4π5, then cot−1x+cot−1y equalsr. π/4d. tan−117+2tan−113=s. π

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