Prove that: `sin^-1(3/5)-cos^-1(12/13)=sin^-1(16/65)`

1.	Prove that: `sin^-1(3/5)-cos^-1(12/13)=sin^-1(16/65)`
Answer» LHS `sin^(-1)(3/5)-cos^(-1)(12/13)` Let`cos^(-1)(12/13)=theta` `costheta=12/13` `sintheta=5/13` `theta=sin^(-1)(5/13)` `sin^(-1)(3/5)-theta` `sin^(-1)(3/5)-sin^(-1)(5/13)` `sin^(-1)x-sin^(-1)y` `(xsqrt(1-y^2)-ysqrt(1-x^2))` `sin^(-1)(3/5sqrt(1-(5/13)^2)-5/13sqrt(1-(3/5)^2)` `sin^(-1)(3/512/13-5/13*4/5)` `sin^(-1)(36/65-20/65)` `sin^(-1)(16/65)=RHS`.

Discussion

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