Trig. Identities & Calculus Standard Results

Question 1

sin(A+B)=

Answer 1

sinAcosB + cosAsinB

Question 2

sin(A-B)=

Answer 2

sinAcosB - cosAsinB

Question 3

cos(A+B)=

Answer 3

cosAcosB - sinAsinB

Question 4

cos(A-B)=

Answer 4

cosAcosB + sinAsinB

Question 5

tan(A+B)=

Answer 5

tanA + tanB / 1 - tanAtanB

Question 6

tan(A-B)=

Answer 6

tanA - tanB / 1 + tanAtanB

Question 7

sin2A=

Answer 7

2sinAcosA

Question 8

cos2A=

Answer 8

cos^2A - sin^2A
2cos^2A - 1
1-2sin^2A

Question 9

tan2A=

Answer 9

2tanA / 1 - tan^2A

Question 10

sin^2x + cos^2x =

Answer 10

1

Question 11

1 + tan^2x =

Answer 11

sec^2x

Question 12

1 + cot^2x =

Answer 12

cosec^2x

Question 13

secx =

Answer 13

1/cosx

Question 14

cosecx =

Answer 14

1/sinx

Question 15

cotx =

Answer 15

1/tanx

Question 16

tanx =

Answer 16

sinx/cosx

Question 17

cotx =

Answer 17

cosx/sinx

Question 18

f(x) = sinx
f’(x) =

Answer 18

cosx

Question 19

f(x) = cosx
f’(x) =

Answer 19

-sinx

Question 20

f(x) = a^x
f’(x) =

Answer 20

a^x . ln(a)

Question 21

f(x) = e^x
f’(x) =

Answer 21

e^x

Question 22

f(x) = ln(f(x))
f’(x) =

Answer 22

f’(x) / f(x)

Question 23

f(x) = f(g(x))
f’(x) =

Answer 23

f’(g(x))g’(x)
chain rule

Question 24

f(x) = f(x)g(x)
f’(x) =

Answer 24

f’(x)g(x) + f(x)g’(x)
u’v + uv’
product rule

Question 25

f(x) = f(x)/g(x)
f’(x) =

Answer 25

f’(x)g(x) - f(x)g’(x) / (g(x))^2
u’v - uv’ / v^2
quotient rule

Question 26

f(x) = tanx
f’(x) =

Answer 26

sec^2(x)

Question 27

f(x) = secx
f’(x) =

Answer 27

sec(x)tan(x)

Question 28

f(x) = cotx
f’(x) =

Answer 28

-cosec^2(x)

Question 29

f(x) = cosecx
f’(x) =

Answer 29

-cosec(x)cot(x)