Question

The principal value of sin^-1 1/√5 + sin^-1 2/√5 is equal to​

Answer 1

Answer:

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Step-by-step explanation:

Solution :

To simplify, 3⋅tan−1(12)+2⋅tan−1(15)+sin−1(14266⋅5–√) Consider, sin−1(14266⋅5–√), from its general triangle: P=142 H=66⋅5–√ B=P2+H2−−−−−−−√ B=31 ∴sin−1(14266⋅5–√)=tan−1(14231) We have, 3⋅tan−1(12)+2⋅tan−1(15)+tan−1(14231) We know, 2tan−1x=tan−1(2x1−x2)and,tan−1x+tan−1y=tan−1(x+y1−xy) So, 2tan−1(15)=tan−1(251−125)=tan−1(25⋅2524)=tan−1(512) 2tan−1(12)=tan−1(11−14)=tan−1(43) 3tan−1(12)=tan−1(12)+tan−1(43) =tan−1(43+121−29) =tan−1(116⋅3)=tan−1(112) 3⋅tan−1(12)+2⋅tan−1(15)=tan−1(112)+tan−1(512)=tan−1(112+5121−5524)=tan−1(7112−3124)+π=tan−1(−14231)+π 3⋅tan−1(12)+2⋅tan−1(15)+tan−1(14231)=tan−1(−14231)+π+tan−1(14231)=−tan−1(14231)+π+tan−1(−14231)=π

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