⚡
Quick TrainerTrigonometric Identities and Their Equivalents
Recall the equivalent expression for each fundamental trigonometric identity.
Math29 items4 levelsDifficulty 3/5
Free · no signup · works on any device
Levels
Start easy — harder levels unlock as you improve, or jump ahead anytime.
1
Reciprocal & Quotient
6 items
2
Pythagorean & Even-Odd
8 items
3
Double & Sum/Difference
10 items
4
Half-Angle & Cofunction
5 items
All 29 cards
csc x = ?
1/sin x
sec x = ?
1/cos x
cot x = ? (reciprocal form)
1/tan x
tan x = ? (quotient form)
sin x / cos x
cot x = ? (quotient form)
cos x / sin x
sin x · csc x = ?
1
sin²x + cos²x = ?
1
1 + tan²x = ?
sec²x
1 + cot²x = ?
csc²x
1 − sin²x = ?
cos²x
sec²x − tan²x = ?
1
sin(−x) = ?
−sin x
cos(−x) = ?
cos x
tan(−x) = ?
−tan x
sin(2x) = ?
2 sin x cos x
cos(2x) = ? (in sin and cos)
cos²x − sin²x
cos(2x) = ? (in cos only)
2cos²x − 1
cos(2x) = ? (in sin only)
1 − 2sin²x
tan(2x) = ?
2 tan x / (1 − tan²x)
sin(a + b) = ?
sin a cos b + cos a sin b
sin(a − b) = ?
sin a cos b − cos a sin b
cos(a + b) = ?
cos a cos b − sin a sin b
cos(a − b) = ?
cos a cos b + sin a sin b
tan(a + b) = ?
(tan a + tan b)/(1 − tan a tan b)
sin²x = ? (power-reduction)
(1 − cos 2x)/2
cos²x = ? (power-reduction)
(1 + cos 2x)/2
sin(90° − x) = ?
cos x
cos(90° − x) = ?
sin x
tan(90° − x) = ?
cot x
