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Home > Calculus calculators > Simplifying trigonometric equations, proving identities calculator

Method and examples

Trigonometry

Method

1. Simplifying trigonometric equations, proving identities

Expression

`sin^2(30)*cos^2(60)`
`sin(30)*cos(60)+sin(30)*cos(60)`
`sin(30)*csc(30)-sin(60)*csc(60)`
`2sin^2(30)*3cos^2(60)`
`(2tan(60))/(1+tan^2(60))`
`(3sec(60)+2tan(45)+csc(30))/(sin^2(60)+cot^2(45))`
`(3sec(60)+2tan(45)+csc(30))(sin^2(60)+cot^2(45))`
`sin(30)*cos(45)*tan(60)=sin(45)*cos(60)*cot(30)`
`tan(45)*sec(72)*sin(58)=cos(32)*csc(18)`
`sin^2(34)-cot^2(46)-cos^2(56)+tan^2(44)=sec^2(62)-csc^2(28)`
`sin(30)*cos(45)*tan(60)=sin(45)*cos(60)*cot(30)`
`tan(45)*sec(72)*sin(58)=cos(32)*csc(18)`
`sin^2(34)-cot^2(46)-cos^2(56)+tan^2(44)=sec^2(62)-csc^2(28)`
`sin^2(50)+sin^2(40)=1`
`sin(35)*sec(55)-cos(55)*csc(35)=tan(25)-cot(65)`
`2sin(30)+2tan(45)-3cos(60)-2cos^2(30)=0`
`2sec^2(x)-2`
`sin(x)sec(x)`
`sin(x)cot(x)`
`cot(x)sin(x)`
`tan(x)+cot(x)`
`cos(x)+cot(x)`
`tan(x)sin(x)+cos(x)`
`cot^4(x)+cot^2(x)`
`cos^2(x)csc^2(x)-cos^2(x)`
`tan^2(x)-sin^2(x)`
`(csc(x)-sin(x))(sec(x)-cos(x))`
`(tan(x)+cot(x))(sec(x)-cos(x))(csc(x)-sin(x))`
`1+1/tan^2(x)`
`csc(x)/cos(x)-cos(x)/sin(x)`
`sec(x)/2(tan(x)+cot(x))`
`sec(x)/(2(tan(x)+cot(x)))`
`(tan^2(x)-cot^2(x))/(sin^2(x)-cos^2(x))`
`(tan^2(x)+cot^2(x))/(tan^2(x)-cot^2(x))`
`(tan^2(x)-cot^2(x))/(tan^2(x)+cot^2(x))`
`(3sin(x)+5cos(x))^2+(3cos(x)-5sin(x))^2`
`(1+cos(x))/sin(x)+sin(x)/(1+cos(x))`
`sin^2(x)cos(x)+sin^3(x)+cos^2(x)sin(x)+cos^3(x)`
`(sin^4(x)-cos^4(x))/(sin^2(x)-cos^2(x))`
`5cos^2(x)+2sin^2(x)`
`2cos^2(x)+sin^2(x)`
`(sin^4(x)+cos^4(x))`

2. Find the value of all the other five trigonometric functions or solve expression

If = then

1. Find the value of all the other five trigonometric functions sin(x)cos(x)tan(x) csc(x)sec(x)cot(x)	2. Solve expression
If `sin(x)=5/13` then find other trigonometry If `cos(x)=12/13` then find other trigonometry If `tan(x)=5/12` then find other trigonometry If `csc(x)=13/5` then find other trigonometry If `sec(x)=13/12` then find other trigonometry If `cot(x)=12/5` then find other trigonometry	If `sin(x)=3/5` then solve `cos(x)csc(x)+tan(x)sec(x)` If `tan(x)=1/2` then solve `(1-tan^2(x))/(1+tan^2(x))+(2tan(x))/(1+tan^2(x))` If `sin(x)=4/5` then solve `(1-sin(x))/cos(x)+cos(x)/(1-sin(x))` If `cos(x)=3/5` then solve `(1-sin(x))/cos(x)+cos(x)/(1-sin(x))`

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