Question

find the solution
$tan^{ - 1} - sec^{ - 1} ( - 2)$
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Answer 1

Answer:

Solution

sec−1(−x)=π−sec−1xsec-1(-x)=π-sec-1x

sec−1(−2)=π−sec−12sec-1(-2)=π-sec-12

and the principal value of sec−12 is π3sec-12 is π3

∴Sec−1(−2)=π−π/3∴Sec-1(-2)=π-π/3

=2π3=2π3

Also, tan−1(−13–√)=−tan−1(13–√),(∵tan−1(−x)=−tan−1x)tan-1(-13)=-tan-1(13),(∵tan-1(-x)=-tan-1x)

=−π6=-π6

∴sec−1(−2)+tan−1(−13–√)∴sec-1(-2)+tan-1(-13)

=2π3