1.

Prove that:`tan^(-1)(4/5)+cos^(-1)(12/13)=cos^(-1)(33/65)`

Answer» We have,
LHS `=cos^(-1)4/5+cos^(-1)12/13`
`=cos^(-1){(4/5 xx 12/13)-sqrt(1-(4/5)^(2)).sqrt(1-(12/13)^(2))}`
`=cos^(-1){48/65-sqrt(1-(16/25)).sqrt(1-144/169)}`
`=cos^(-1){48/65-sqrt(9/25).sqrt(25/169)}`
`=cos^(-1){48/65-3/5 xx 5/13}=cos^(-1)(48/65-15/65)`
`=cos^(-1){12/17-sqrt(64/289).sqrt(9/25)}=cos^(-1){12/17 -8/17 xx 3/5)`
`=cos^(-1){12/17-24/85}=cos^(-1)(36/85)=`RHS
Hence, `sin^(-1)8/17+sin^(-1)3/5=cos^(-1)36/85`.


Discussion

No Comment Found

Related InterviewSolutions