Trigonometry all formulas

                     

Hello aspirants,

Today I am here to give you all trigonometry formulas. I am not providing you images of formule because you can just save the image and you learn learn that on your mood and whenever you take yourp in your hand I am pretty sure that you can't focus on formulas.

So it is good that you wrote it down I your separate formula copy. I make it pardon that in you separate formula notebook .

Because it is beneficial for you if you make separate formula note book then at last moment when you to revise you don't have to go through whole book.make sure that in your formula note book don't do any question just write down the formula and revise it continuously.

So let's start with all the Josh!!!

.sin²x+cos²x=1

.1+tan²x=sec²x

.1+cot²x=cosec²x

.sin(-x)= -sinx               .cos(-x)=cosx

.cosec(-x)= -cosecx.      .sec(-x)=secx

.tan(-x)= -tanx

.cot(-x)= -cotx

>Sin(x+y)=sinx cosy+cosx siny

>Sin(x-y)=sinx cosy- cosx siny

>Cos(x+y)=cosx cosy-sinx siny

>Cos(x-y)=cosx cosy+ sinx siny

>Tan(x+y)= tanx + tany.

                     1-tanx tany

>Tan(x-y)=tanx - tany.

                   1+tanx tany 

>Cot(x+y)=cotx coty -1

                   Coty + cotx

>Cot(x-y)=cotx coty +1

                   Coty - cotx 
>Tan(x+y+z)=tanx+tany+tanz-tanxtanytanz                          1-tanxtany-tanytanz-tanxtanz

Now from here we begin with most important and confusing formula and conversion.
 For 90° change (trigonometry ratios change)

>Sin(90°-x)  =cosx.         >Cos(90°-x)=sinx
>Tan(90°-x)=cotx.          >Cot(90°-x)=tanx
>Sec(90°-x)= cosec x.    >Cosec(90°-x)=secx

>Sin(90+x)=cosx.          >Cos(90°+x)= -sinx
>Cosec(90°+x)=secx.    >Tan(90°+x)= -cotx
                                        >Cot(90°+x)= -tanx
                                       >Sec(90°+x) = -cosecx
For 180° change ( trigonometry ratios doesn't change)

>Sin(π-x)=sinx.                 >Cos(π-x)= -cosx     
>Cosec(π-x)=cosecx.        >Tan(π-x)=-tanx
                                            >Cot(π-x) =-cotx
                                            >Sec(π-x)=-secx

>Tan(π+x)=tanx.              >Sin(π+x)= -sinx
>Cot(π+x)=cotx                >cos(π+x)= -cosx
                                           >Sec(π+x)= -secx
                                         >Cosec(π+x)= -cosecx
 For 270°change(trigonometric ratio change)

>Tan(270°-x)= cotx.           >Sin(270°-x)= -cosx
>Cot(270°-x)= tanx.           >Cos(270°-x)= -sinx
                                           >Sec(270°-x)=-cosecx
                                           >Cosec(270-x)=-secx

>Cos(270°+x) =sinx.       >Sin(270°-x)=-cosx
>Sec(270°+x)=cosecx.   >Cosec(270°-x)= -secx
                                         >Tan(270°-x)=-cotx
                                         >Cot(270°-x) = -tanx

For 360°change (trigonometry ratios doesn't change)

>Cos(2π-x)=cosx.             >Sin(2π-x)= -sinx
>Sec(2π-x)=secx.           >Cosec(2π-x)= -cosecx
                                         >Tan(2π-x)= - tanx
                                          >Cot(2π-x)= -cotx

>Sin(2πn+x)=sinx.      >Cos(2πn+x)=cosx
>Sec(2πn+x)=secx.     >Cosec(2πn+x)=cosecx
>Tan(2πn+x)=tanx.    >Cot(2πn+x)=cotx



>Sin²x - sin²y=sin(x+y)sin(x-y)
>Cos²x - cos²y=cos(x+y)cos(x-y)
>Sin²x - cos²y cos(x+y)cos(x-y)

>2sinx cosy=sin(x+y) + sin(x-y)
>2cosx cosy=sin(x+y) - sin(x-y)
>2cosx cosy=cos(x+y) + cos(x-y)
>2sinx siny=cos(x-y) - cos(x+y)

>Sinc+SinD=2sin( C+D\2) cos(C-D\2)
                                           
>Sinc-SinD=2cos( C-D\2) sin(C+D\2)
                                             
>Cosc+CosD=2cos( C+D\2) cos(C-D\2)
                                           
>Cosc-CosD=-2sin( C+D\2) sin(C-D\2)