LIST OF FORMULA

TRIGONOMETRIC IDENTITIES

sina sinb=12

[cos (a−b )−cos (a+b)]

cos acosb=12

[cos (a−b )+cos(a+b)]

sinacos b=12

[sin (a−b )+sin(a+b)]

sina+sinb=2 sin12

(a+b ) cos12(a−b)

sina−sinb=2 sin12

(a−b ) cos12(a+b)

cos a+cosb=2 cos12

(a+b ) cos12(a−b)

cos a−cos b=−2sin12

(a+b ) sin12(a−b)

sin (a+b )=sinacosb+cosa sinbsin (a−b )=sinacosb−cos a sinbcos (a+b )=cosa cosb−sina sinbcos (a−b )=cos acosb+sina sinb

tan (a+b )= tan(a)+ tan(b)1−tan (a ) tan (b)

tan (a−b )=tan (a )−tan (b)

1+tan (a ) tan (b)

sin2a+cos2a=1tan2a+1=sec2a1+cot2a=csc2acos (2a )=cos2a−sin2acos (2a )=2cos2a−1cos (2a )=1−2sin2asin (2a )=2sin acosa

TRIGONOMETRIC FUNCTIONS

DIFFERENTIATION FORMULA INTEGRATION FORMULA

1 . ddx

[x ]=1

2 . ddx [ xr+1

r+1 ]=xr (r≠−1 )

3 . ddx

[bu ]=bu ln b⋅dudx

4 .ddx

[eu ]=eu⋅dudx

5 . ddx

[ ln u ]=1u⋅dudx

6 . ddx [ logbu ]=1

u ln b⋅dudx

7 . ddx

[ sin x ]=cos x

8 . ddx

[−cos x ]=sin x

9 . ddx

[ tan x ]=sec2 x

10 . ddx

[−cot x ]=csc2 x

11. ddx

[ sec x ]=sec x tan x

12 . ddx

[−csc x ]=csc x cot x

∫ dx=x+C∫ xr dx=x

r+1

r+1+C (r≠1 )

∫cos xdx=sin x+C

∫sin xdx=−cos x+C

∫sec2 xdx=tan x+C

∫csc2 xdx=−cot x+C

∫sec x tan xdx=sec x+C

∫csc xcot xdx=−csc x+C

∫csc xdx=ln|csc x−cot x|+C

∫sec xdx=ln|sec x+ tan x|+C

Reduction Formula

∫sinn xdx=−1n

sinn−1 x cos x+n−1n ∫sinn−2 xdx

∫cosn xdx=1n

cosn−1 x sin x+n−1n

∫ cosn−2 xdx

∫ tann xdx=tann−1 xn−1

−∫ tann−2 xdx

∫secn xdx=secn−2 x tan xn−1

+n−2n−1

∫secn−2 xdx

INVERSE TRIGONOMETRIC FUNCTIONS FORMULAS

DIFFERENTIATION

ddx

[sin−1u ]=1

√1−u2

dudx

ddx

[cos−1u ]=−1

√1−u2

dudx

ddx

[ tan−1u ]=11+u2

dudx

ddx

[cot−1u ]=−1

1+u2

dudx

ddx

[sec−1u ]=1

|u|√u2−1

dudx

ddx

[csc−1u ]=−1

|u|√u2−1

dudx

INTEGRATION

∫1

a2+u2du=

1a

tan−1ua

+C

∫1

√a2−u2du=sin−1u

a+C

∫1

u√u2−a2du=1

asec−1|u

a|+C