INDENTITIES UNIT 4

Prove the identities

100

(cosx-1)(sinx+1)=0

x=0+2 k pi

x=3pi/2+2 k pi

200

2sin2x=1-sinx 

pi/6 +2 k pi

5pi/6 +2 k pi

3pi/2 +2 k pi

300

( cscx + secx) / (sinx + cosx) = cotx + tanx

prove both side to be 1 / (sinx cosx)

400

sec² x - cot² x (pi/2 - x) = 1

sec² x - cot² x = 1

500

sin 4x = 8 cos³ x sinx - 4 cosx sinx

1. prove both side to be 4 sinx cosx cos2x

2. prove the left side to be = to the right

Name the identity

100

cot(x)=cos(x)/sin(x)

reciprocal identity for cotangent

200

cos²+sin²=1

pythagorean identity

300

sin(-x)=- sin x

Even-Odd identity of sin

400

Cos(2x)=cos²x - sin²x

Double angle formula

500

sin²x=1-cos(2x)/2

Power-reducing formula for sine

Solve the identity

100

sin 20^。cos 40^。+ sin 40^。sin 20^。

root 3 /2 

200

tan x = -1

-pi/4 + k pi

3pi/4 + k pi

300

sin x = 2/3

sin^-1(2/3) + 2 k pi

pi - sin^-1(2/3) + 2 k pi

400

4 sin² x = 3

+/- pi/3 + 2 k pi

+/- 2pi/3 + 2 k pi

500

sin x - 1 = cos x

0 + 2 k pi

pi + 2 k pi

pi/2 + 2 k pi

Simplify the indentity

100

sin2x / (1- cos²x)

2 cotx

200

(1 + cotx) / cscx

sin x + cosx

300

2cos (x+ pi/6) + sinx

root 3 (cosx)

400

sec²x cotx - cotx

tan x

500

(1/ sinx + 1) + (1/ cscx+ 1)

1