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Verifying the Identities

100

1 + tan²Θ / secΘ = sec Θ 

Sec Θ = sec Θ
✅

200

Sin2x = 2cotx Sin²x

Sin2x

✅

300

csc² Θ - cos² Θ csc² Θ =1 

1 = 1

✅

400

Sin(x + π) = -sinx

-sinx=-sin x 

✅

Solving Trigonometric Equations

100

Sec Θ csc Θ + √2 csc Θ = 0

No Solution 

Θ= 3π/ 4 + 2π k
Θ = 5π/ 4 + 2π k

200

Cos²x + sine = 1

X = 0 + π k

x= π/2 + 2πk 

300

Cosx + √3 = -cos x

X = 150° + 360 K

X = 210° + 360 K

400

2 sin Θ cos Θ + cos Θ = 0

Θ= 90° + 180 k

Θ = 210° + 360 k

Θ = 330° + 360 k

Solving for Degree

100

4 sin²x - 1 = 0

X = 30°, 150°, 210°, 330°

200

Sinxcosx - cosx+sinx-1 = 0

90°

180°

300

6sec² x -5 = 3

x = 30°, 150°, 210°, 330°

400

4cotx + 9 = 5cotx +8

X = 45°, 225°

Sum and Difference Formulas

100

sinx + cos² x /sinx 

Cscx

200

1/ secx+1 - 1/secx-1 

0

300

tan(x - π) = tan x

tan x = tan x 

400

Sin (x - π/2 ) = - cos x

- cos x = - cos x

Bonus!

500

Find all solutions of 

Cos x + 1 = sin x in the interval [0, 2π]

X = π/2, 3π / 2

x = π