Formulas to remember

Question 1

How to prove Tan 2A

Answer 1

Tan (2A) = Tan A + Tan A

= Tan A + Tan A / 1 - TanATanA

= 2tanA / 1 - Tan^2A

Question 2

What are the double angle formula?

Answer 2

Sin2A = 2sinAcosA
Cos2A = cos^2A - sin^2A
               = 1 - 2Sin^2A
                 = 2Cos^2A - 1
Tan2A = 2TanA / 1 - Tan^2A

Question 3

What are the compound angle formula?

Answer 3

Sin (A+B) = SinACosB + CosASinB
Cos (A+B) = CosACosB - SinASinB
Tan (A+B) = TanA + TanB / 1 - TanATanB

If the sign changes in the bracket, the signs change throughout

Question 4

How to prove Tan (A+B) using Sin (A+B) and Cos (A+B)

Answer 4

= Sin (A+B)
Cos (A+B)

SinACosB + CosASinB
CosACosB - SinASinB

Divide every single term by CosACosB

What’s left over

SinA/SinB + SinB/CosB
CosB/CosB - SinASinB/CosACosB

Which becomes

TanA + TanB
1 - TanATanB

= Tan (A+B)

Question 5

cos^2 + sin^2 = what?

Answer 5

1

Question 6

sec^2 = what?

Answer 6

1 + tan^2

Question 7

cosec^2 = what?

Answer 7

1 + cot^2

Question 8

Differential of sinx

Answer 8

cosx

Question 9

Differential of cosx

Answer 9

-sinx

Question 10

Differential of e^kx

Answer 10

ke^kx

Question 11

Differential of lnx

Answer 11

1/x

Question 12

What’s the product rule

Answer 12

u’v + v’u

Question 13

What’s the chain rule

Answer 13

Make the second part u, times the differential of u by the main body and sub u back in

Question 14

What’s the quotient rule

Answer 14

U’v + v’u / v^2

Question 15

How to change a double angle in the format Rsin(x + a)

Answer 15

R = Root /A^2 + B^2
a = tan-1 (B/A)