Show:
Reciprocal Identity
Even-Odd Identity
Pythagorean Identity
Mix
100

Simplify the following expression:

sin x cot x

cos x

100

Write in terms of sine and cosine.

csc(-x)

- 1 / sin x

100

Simplify the following expression:

1 - sin^2 (x) 

cos^2(x)

100

Verify the following identity:

cos(-x) - sin(-x) = cos x + sin x

LHS:

cos(-x) = cos x

sin(-x) = - sin x

cos x - (-sin x)

cos x + sin x = cos x + sin x


200

Simplify the following expression:

tan x cot x

1

200

Write in terms of sine and cosine.

1 / sec(-x)

cos x

200

Simplify the following expression:

sin^2(x) / cos^2(x) - sec^2(x)

1

200

Verify the following identity:

(sin x + cos x)^2 = 1 + 2 sin x cos x

LHS:

sin^2(x) + sin x cos x + sin x cos x + cos^2(x)

(sin^2(x) + cos^2(x)) + 2 sin x cos x

1 + 2 sin x cos x = 1 + 2 sin x cos x

300

Verify the following identity:

sin x / tan x = cos x

sin x cot x

sin x (cos x / sin x)

cos x

300

Write in terms of sine and cosine.

cot(-x)

- 1 / tan x
300

Simplify the following expression:

1 + cot^2(x) 

csc^2(x)

300

Verify the following identity:

cos v / (sec v sin v) = csc v - sin v

LHS:

cos^2(v) / sin v

(1 - sin^2(v)) / sin v

RHS:

1 / sin v - sin v

(1 - sin^2(v)) / sin v

400

Verify the following identity: 

(cos u sec u) / tan u = cot u

cos u / (cos u tan u)

1 / tan u

cot u

400

Write in terms of sine and cosine.

tan(-x)cot(x)

- 1

400

Simplify the following expression:

1 / cos^2(x) - 1

tan^2(x)

400

Verify the following identity:

(cos x / sec x) + (sin x / csc x) = 1


LHS:

cos x cos x + sin x sin x

cos^2(x) + sin^2(x)

1 = 1