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Prove that 2sin^(-1) (3/5)-cos^(-1)(5/13...

Prove that `2sin^(-1) (3/5)-cos^(-1)(5/13) = cos^(-1)(323/325)`

Text Solution

Verified by Experts

=`2 sin^(-1)(3/5)`
=`2 tan^(-1)(3/4)`
=`tan^(-1)(3/4)+tan^(-1)(3/4)`
=`tan^(-1)(((3/4)+(3/4))/(1-(3/4)(3/4)))`
=`tan^(-1)((24/16)/(7/16))`
=`tan^(-1)(24/7)`
hence proved
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