for Sumi's shop
Trigonometric Identities — Easy Worksheet 2
Grade 12 · MathSheets Name: ____________________ Date: __________
Simplify each expression to a single term such as 1, sin x, cos^2 x or -sin^2 x, or find the exact value asked for.
How to solve
Rewrite everything in sin and cos: tan x = sin x / cos x, sec x = 1 / cos x, csc x = 1 / sin x, cot x = cos x / sin x. Then use sin2 x + cos2 x = 1 (and 1 + tan2 x = sec2 x, 1 + cot2 x = csc2 x) and cancel.
Example
Simplify: 1 + cot2 x
Answer: csc2 x
✓ Correct!
Not quite. The answer is
💡 How to solve: Trigonometric Identities
Rewrite everything in sin and cos: tan x = sin x / cos x, sec x = 1 / cos x, csc x = 1 / sin x, cot x = cos x / sin x. Then use sin2 x + cos2 x = 1 (and 1 + tan2 x = sec2 x, 1 + cot2 x = csc2 x) and cancel.
Try a similar one
Simplify: sec2 x - tan2 x
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Trigonometric Identities
Rewrite everything in sin and cos: tan x = sin x / cos x, sec x = 1 / cos x, csc x = 1 / sin x, cot x = cos x / sin x. Then use sin2 x + cos2 x = 1 (and 1 + tan2 x = sec2 x, 1 + cot2 x = csc2 x) and cancel.
Try a similar one
Simplify: cos x / cot x
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Trigonometric Identities
Rewrite everything in sin and cos: tan x = sin x / cos x, sec x = 1 / cos x, csc x = 1 / sin x, cot x = cos x / sin x. Then use sin2 x + cos2 x = 1 (and 1 + tan2 x = sec2 x, 1 + cot2 x = csc2 x) and cancel.
Try a similar one
Simplify: cos x / cot x
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Trigonometric Identities
Rewrite everything in sin and cos: tan x = sin x / cos x, sec x = 1 / cos x, csc x = 1 / sin x, cot x = cos x / sin x. Then use sin2 x + cos2 x = 1 (and 1 + tan2 x = sec2 x, 1 + cot2 x = csc2 x) and cancel.
Try a similar one
Simplify: cot x · sin x
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Trigonometric Identities
Rewrite everything in sin and cos: tan x = sin x / cos x, sec x = 1 / cos x, csc x = 1 / sin x, cot x = cos x / sin x. Then use sin2 x + cos2 x = 1 (and 1 + tan2 x = sec2 x, 1 + cot2 x = csc2 x) and cancel.
Try a similar one
Simplify: sec2 x - 1
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Trigonometric Identities
Rewrite everything in sin and cos: tan x = sin x / cos x, sec x = 1 / cos x, csc x = 1 / sin x, cot x = cos x / sin x. Then use sin2 x + cos2 x = 1 (and 1 + tan2 x = sec2 x, 1 + cot2 x = csc2 x) and cancel.
Try a similar one
Simplify: sin x / tan x
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Trigonometric Identities
Rewrite everything in sin and cos: tan x = sin x / cos x, sec x = 1 / cos x, csc x = 1 / sin x, cot x = cos x / sin x. Then use sin2 x + cos2 x = 1 (and 1 + tan2 x = sec2 x, 1 + cot2 x = csc2 x) and cancel.
Try a similar one
Simplify: csc x · cos x
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Trigonometric Identities
Rewrite everything in sin and cos: tan x = sin x / cos x, sec x = 1 / cos x, csc x = 1 / sin x, cot x = cos x / sin x. Then use sin2 x + cos2 x = 1 (and 1 + tan2 x = sec2 x, 1 + cot2 x = csc2 x) and cancel.
Try a similar one
Simplify: cot x · sin x
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Log in to save your progress.
Trigonometric Identities — Easy Worksheet 2
Simplify each expression to a single term such as 1, sin x, cos^2 x or -sin^2 x, or find the exact value asked for.