1. If `sin(x)=3/5`, solve `cos(x)csc(x)+tan(x)sec(x)`
Solution:
`sin(x)=3/5` (given)
`cos(x)csc(x)+tan(x)sec(x)=?`
`sin(x)=3/5`, in Quadrant-1
`(1)` `cos^2(x)=1-sin^2(x)`
`=1-(3/5)^2`
`=1-9/25`
`=(25-9)/25`
`=16/25`
`:.cos(x)=sqrt(16/25)=4/5=4/5`
`(2)` `tan(x)=sin(x)/cos(x)=(3/5)/(4/5)=3/5 xx 5/4=3/4=3/4`
`(3)` `csc(x)=1/sin(x)=1/(3/5)=5/3=5/3`
`(4)` `sec(x)=1/cos(x)=1/(4/5)=5/4=5/4`
Now substitute all these expression values in
`cos(x)csc(x)+tan(x)sec(x)`
`=(4/5)(5/3)+(3/4)(5/4)`
`=4/3+15/16`
`=109/48`
`:. cos(x)csc(x)+tan(x)sec(x)=109/48`
This material is intended as a summary. Use your textbook for detail explanation.
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