Standard Results C6,7,9

Question 1

Sec(x) =

Answer 1

1 / cos(x)

Question 2

Cosec (x) =

Answer 2

1 / sin(x)

Question 3

Cot(x) =

Answer 3

1 / tan(x)

Question 4

Equation linking tan^2(x) and sec^2(x)

Answer 4

1 + tan^2(x) = sec^2(x)

Question 5

Equation linking cot^2(x) and cosec^2(x)

Answer 5

1 + cot^2x = cosec^2(x)

Question 6

Order of differentiation for Sin and Cos

Answer 6

Sin to Cos to -Sin to -Cos

Question 7

Order of integration for sin and cos

Answer 7

Sin to -Cos to -Sin to Cos

Question 8

Differential of sinkx

Answer 8

Kcoskx

Question 9

Differential of coskx

Answer 9

-ksinkx

Question 10

Differential of e^x

Answer 10

e^x

Question 11

Differential of e^kx

Answer 11

Ke^kx

Question 12

Differential of Ln(x)

Answer 12

1/x

Question 13

Differential of a^x

Answer 13

A^xlna

Question 14

Differential of a^kx

Answer 14

KA^kxlna

Question 15

Differential of tan(x)

Answer 15

Sec^2(x)

Question 16

Differential of sec(x)

Answer 16

Sec(x)tan(x)

Question 17

Differential of cot(x)

Answer 17

-cosec^2(x)

Question 18

Differential of cosec(x)

Answer 18

-cosecxcotx

Question 19

Sin(a+-b)=

Answer 19

SinaCosb +- CosaSinb

Question 20

Cos(A+-B)

Answer 20

CosAcosB -+ SinASinB

Question 21

Tan(A+-B) =

Answer 21

tanA +- tanB / 1 -+ tanAtanB

Question 22

Sin(2A) =

Answer 22

2sinAcosB

Question 23

Cos(2A) =

Answer 23

Cos^2A - Sin^2A ; 2cos^2A - 1 ; 1-2Sin^2A

Question 24

Tan2A=

Answer 24

(2TanA / 1 -Tan^2A