C3

Question 1

cot∆

Answer 1

cos∆/sin∆ as well as 1/tan∆

Question 2

Where does cot∆ cross between 0 and π

Answer 2

π/2

Question 3

sec(^2)∆

Answer 3

tan(^2)∆+1

Question 4

cosec(^2)∆

Answer 4

cot(^2)∆+1

Question 5

sin(A+B)

Answer 5

sinAcosB+cosAsinB

Question 6

sin(A—B)

Answer 6

sinAcosB-cosAsinB

Question 7

cos(A+B)

Answer 7

cosAcosB-sinAsinB

Question 8

cos(A—B)

Answer 8

cosAcosB+sinAsinB

Question 9

tan(A+B)

Answer 9

(tanA+tanB) / (1—tanAtanB)

Question 10

tan(A—B)

Answer 10

(tanA-tanB) / (1+tanAtanB)

Question 11

sin2A

Answer 11

2sinAcosA

Question 12

cos2A

Answer 12

cos(^2)A—sin(^2)A or 2cos(^2)A—1 or

1-2sin(^2)A

Question 13

tan2A

Answer 13

(2tanA)/(1—tan(^2)A

Question 14

asin∆±bcos∆

Answer 14

Rsin(∆±Ω) where R>0 and 0<90 where RcosΩ=a, RsinΩ=b and R=√(a(^2)+b(^2))

Question 15

acos∆±bsin∆

Answer 15

Rcos(∆±Ω) where R>0 and 0<90 where RcosΩ=a, RsinΩ=b and R=√(a(^2)+b(^2))

Question 16

2sinAcosB

Answer 16

sin(A+B)+sin(A—B)

Question 17

2cosAcosB

Answer 17

cos(A+B)+cos(A—B)

Question 18

2cosAsinB

Answer 18

sin(A+B)—sin(A—B)

Question 19

2sinAsinB

Answer 19

—[cos(A+B)—cos(A—B)]

Question 20

sinP+sinQ

Answer 20

2sin((P+Q)/2)cos((P—Q)/2)

Question 21

cosP+cosQ

Answer 21

2cos((P+Q)/2)cos((P—Q)/2)

Question 22

sinP—sinQ

Answer 22

2cos((P+Q)/2)sin((P—Q)/2)

Question 23

cosP—cosQ

Answer 23

—2sin((P+Q)/2)sin((P—Q)/2)

Question 24

y=f(x)

Answer 24

F’(x)=nf(x)

Question 25

y=f[g(x)]

Answer 25

F'(x)=f'[g(x)]g'(x)

Question 26

y=uv

Answer 26

F'(x)=u(dv/dx)+v(du/dx)

Question 27

y=u/v

Answer 27

F'(x)=(v(du/dx)—u(dv/dx))/v(^2)

Question 28

y=e(^f(x))

Answer 28

F'(x)=f'(x)e(^f(x))

Question 29

y=ln(x)

Answer 29

F'(x)=1/x

Question 30

y=ln(f(x))

Answer 30

F'(x)=(f'(x))/(f(x))

Question 31

y=tanx

Answer 31

F'(x)=sec(^2)x

Question 32

y=cosecx

Answer 32

F'(x)=—cosecxcotx

Question 33

y=secx

Answer 33

F'(x)=secxtanx

Question 34

y=cotx

Answer 34

F'(x)=—cosec(^2)x