1. Find value of `tan(x)+cot(x)`
Solution:
`tan(x)+cot(x)`
`=tan(x)+cot(x)`
`=((sin(x))/(cos(x))+(cos(x))/(sin(x)))`
`=(sin^(2)(x)+cos^(2)(x))/(cos(x)sin(x))`
`=(1)/(cos(x)sin(x))`
`=sec(x)csc(x)`
2. Find value of `tan^2(x)-sin^2(x)`
Solution:
`tan^2(x)-sin^2(x)`
`=tan^(2)(x)-sin^(2)(x)`
`=((sin^(2)(x))/(cos^(2)(x))-sin^(2)(x))`
`=sin^(2)(x)(1/(cos^(2)(x))-1)`
`=(sin^(2)(x)(1-cos^(2)(x)))/(cos^(2)(x))`
`=(sin^(2)(x)(sin^(2)(x)))/(cos^(2)(x))`
`=tan^(2)(x)sin^(2)(x)`
3. Find value of `csc(x)/cos(x)-cos(x)/sin(x)`
Solution:
`csc(x)/cos(x)-cos(x)/sin(x)`
`=(csc(x))/(cos(x))-(cos(x))/(sin(x))`
`=((1/(sin(x)))/(cos(x))-(cos(x))/(sin(x)))`
`=(1/(cos(x))-cos(x))/(sin(x))`
`=(1-cos^(2)(x))/(sin(x)cos(x))`
`=(sin^(2)(x))/(sin(x)cos(x))`
`=tan(x)`
4. Find value of `sec(x)/2(tan(x)+cot(x))`
Solution:
`sec(x)/2(tan(x)+cot(x))`
`=(sec(x)(tan(x)+cot(x)))/2`
`=((1/(cos(x)))(((sin(x))/(cos(x)))+((cos(x))/(sin(x)))))/2`
`=((sin^2(x)+cos^2(x))/(cos(x)sin(x)))/(2cos(x))`
`=(1/(cos(x)sin(x)))/(2cos(x))`
`=1/(2cos^2(x)sin(x))`
`=(sec^2(x)csc(x))/2`
5. Find value of `csc(x)/cos(x)-cos(x)/sin(x)`
Solution:
`csc(x)/cos(x)-cos(x)/sin(x)`
`=(csc(x))/(cos(x))-(cos(x))/(sin(x))`
`=(1/(sin(x)))/(cos(x))-(cos(x))/(sin(x))`
`=(1/(cos(x))-cos(x))/(sin(x))`
`=(1-cos^2(x))/(sin(x)cos(x))`
`=(sin^2(x))/(sin(x)cos(x))`
`=tan(x)`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
