1. Find value of `sin(30)*cos(60)+sin(30)*cos(60)`
Solution:
`sin(30)*cos(60)+sin(30)*cos(60)`
`=sin(30)cos(60)+sin(30)cos(60)`
`=(1/2)*(1/2)+(1/2)*(1/2)`
`=1/4+1/4`
`=1/2`
2. Find value of `sin(30)*csc(30)-sin(60)*csc(60)`
Solution:
`sin(30)*csc(30)-sin(60)*csc(60)`
`=sin(30)csc(30)-sin(60)csc(60)`
`=(1/2)*(2)-(sqrt(3)/2)*(2/sqrt(3))`
`=1-1`
`=0`
3. Find value of `(2tan(60))/(1+tan^2(60))`
Solution:
`(2tan(60))/(1+tan^2(60))`
`=(2tan(60))/(1+tan^2(60))`
`2tan(60)=2sqrt(3)`
`=2tan(60)`
`=2*(sqrt(3))`
`=2sqrt(3)`
`1+tan^2(60)=4`
`=1+tan^2(60)`
`=1+(sqrt(3)^2)`
`=1+3`
`=4`
`=(2sqrt(3))/(4)`
`=(sqrt(3))/2`
4. Find value of `(3sec(60)+2tan(45)+csc(30))/(sin^2(60)+cot^2(45))`
Solution:
`(3sec(60)+2tan(45)+csc(30))/(sin^2(60)+cot^2(45))`
`=(3sec(60)+2tan(45)+csc(30))/(sin^2(60)+cot^2(45))`
`3sec(60)+2tan(45)+csc(30)=10`
`=3sec(60)+2tan(45)+csc(30)`
`=3*(2)+2*(1)+(2)`
`=6+2+2`
`=10`
`sin^2(60)+cot^2(45)=7/4`
`=sin^2(60)+cot^2(45)`
`=((sqrt(3)/2)^2)+(1^2)`
`=3/4+1`
`=7/4`
`=(10)/(7/4)`
`=40/7`
5. Find value of `2sin(30)+2tan(45)-3cos(60)-2cos^2(30)`
Solution:
`2sin(30)+2tan(45)-3cos(60)-2cos^2(30)`
`=2sin(30)+2tan(45)-3cos(60)-2cos^2(30)`
`=2*(1/2)+2*(1)-3*(1/2)-2*((sqrt(3)/2)^2)`
`=1+2+(-3)/2+(-3)/2`
`=0`
6. Prove result `sin(30)*cos(45)*tan(60)=sin(45)*cos(60)*cot(30)`
Solution:
LHS `=sin(30)cos(45)tan(60)`
`=(1/2)*(1/sqrt(2))*(sqrt(3))`
`=(sqrt(3))/(2sqrt(2))`
RHS `=sin(45)cos(60)cot(30)`
`=(1/sqrt(2))*(1/2)*(sqrt(3))`
`=(sqrt(3))/(2sqrt(2))`
Result is proved...
This material is intended as a summary. Use your textbook for detail explanation.
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