1. Prove result `sin^2(34)-cot^2(46)-cos^2(56)+tan^2(44)=sec^2(62)-csc^2(28)`
Solution:
LHS `=sin^2(34)-cot^2(46)-cos^2(56)+tan^2(44)`
`cot(46)=tan(44)` and `cos(56)=sin(34)`
`cot(46)=cot(90-44)=tan(44)`
`cos(56)=cos(90-34)=sin(34)`
`=sin^2(34)-tan^2(44)-sin^2(34)+tan^2(44)`
`=0-> (1)`
RHS `=sec^2(62)-csc^2(28)`
`sec(62)=csc(28)`
`sec(62)=sec(90-28)=csc(28)`
`=csc^2(28)-csc^2(28)`
`=0-> (2)`
from (1) and (2)
Result is proved...
2. Prove result `tan(45)*sec(72)*sin(58)=cos(32)*csc(18)`
Solution:
LHS `=tan(45)sec(72)sin(58)`
`sec(72)=csc(18)` and `sin(58)=cos(32)`
`sec(72)=sec(90-18)=csc(18)`
`sin(58)=sin(90-32)=cos(32)`
`=1csc(18)cos(32)`
`=csc(18)cos(32)`
`=`RHS
`:.` Result is proved...
3. Prove result `sin^2(50)+sin^2(40)=1`
Solution:
LHS `=sin^2(50)+sin^2(40)`
`sin(50)=cos(40)`
`sin(50)=sin(90-40)=cos(40)`
`=cos^2(40)+sin^2(40)`
`=1`
`=`RHS
`:.` Result is proved...
This material is intended as a summary. Use your textbook for detail explanation.
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