1.COS(A+B)=cosAcosB-sinAsinB

2.cos(A-B)=cosAcosB+sinAsinB

3.sin(A+B)=sinAcosB+cosAsinB

4.sin(A-B)=sinAcosB-cosAsinB

5.tan(A+B)= (tanA+tanB)/(1-tanAtanB)

6.tan(A-B)= (tanA-tanB)/(1+tanAtanB)      

Single angles

1sinx=3sin(x/3)-4sin³ (x/3)

          =2sin(x/2)cos(x/2)

2.cosx=cos²(A/2)-sin²(A/2)

             =1-2sin²(A/2)

             =2cos²(A/2)            

             =(1-tan²(x/2)/ (1+tan²(x/2)          

3.tanx=(2tan(x/2))÷(1-tan² (x/2))

           =(3tan(x/2))-(tan³( x/2))÷(1-3tan⁴( x /2))

 Double angles

1.sin2x=2sinxcosx=2tanx/1+tan²x

2.cos2x=cos²x-sin²x

              =2cos²x-1=1-2sin²x

              =1-tan² x/1+ tan² x

3.tan2x=2tanx/1-tan²x        

                     

Triple angles

1.sin3x=3sinx-4sin³x

2.cos3x=4cos²x-3cosx

3.tan3x=(3tanx-tan³x)/(1-3tan²x)

Product to sum

1.sinAsinB=1/2[cos(A-B)-cos(A+B)]

2.cosAcosB=1/2[cos(A-B)+cos(A+B)]

3.sinAcosB=1/2[sin(A+B)+sin(A-B)]

4.cosBsinA=1/2[sin(A+B)-sin(A-B)]

Sum to product

1.sinA+sinB=2sin [A+B/2]cos [A-B/2]

2.cosA+cosB=2cos [A+B/2]cos [A-B/2]

3.sinA-sinB=2cos [A+B/(2)]sin [A-B/2]

4.cosA-cosB=-2sin [A+B/2]sin [A-B/2]

Square forumula

Sin² x=(1-cos2x)÷2

Cos² x=(1+cos2x)÷2

Tan² x=(1-cos2x)÷(1+cos2x)

Sin² (x/2)=(1-cosx)÷2

Cos² (x/2)=(1+cosx)÷2

Tan² (x/2)=(1-cosx)÷(1+cosx)

Additional formulas

(1)1+sin2x=(cos x+sin x)

(2)1-sin2x=(cos x-sin x)

(3)1+sinx=(cos(x/2)+sin(x/2)

(4)1-sinx=(cos(x/2)-sin(x/2)

(5)1+cos2x=2 cos² x    

(6)1-cos2x=2 sin² x

(7).(1-cosx)=2sin²(x/2)

(8).(1+cosx)=2cos²(x/2)

When “2” is multiplied

(1).2sinAcosB=sin(A+B)+sin(A-B)

(2)2cosAsinB=sin(A+B)-sin(A-B)

(3)2cosAcosB=cos(A+B)+cos(A-B)

(4)2sinAsinB=cos(A-B)-cos(A+B)

(5)tan(∏+A)=1+tanA/1-tanA

(6)tan(∏-A)=1-tanA/1+tanA

(7)tan^-1  (x+y)/(1-xy)= tan^-1x+ tan^-1x

(8)tan^-1(x-y)/(1+xy)=  tan^-1x- tan^-1x

Algebraic forumula

1.a⁰ =1

2.a²-b²=(a+b)(a-b)

3.a³-b³=(a-b)(a²+ab+b²)

4. a³+b³=(a+b)(a²-ab+b²)

5.(a+b)³=a³+3a²b+3ab²+b³     

6.(a-b)³=a³-3a²b+3ab²-b³