Proofs of Trigonometric Identities

Proving trig identities is a big part of any trigonometry study. Proofs of trigonometric identities are used to show relations between trigonometric functions.Here, you could find all worked proofs of trigonometric identity equations.

Proving Trig Equations

Prove tan(y) / sin(y) = sec(y)
Prove sin(y) + sin(y) cot²(y) = cosec(y)
Prove sin(x) × cos(x) × tan(x) = 1 - cos²(x)
Prove tan(x) + cot(x) = sec(x) csc(x)
Prove (1+cos(x)) / sin(x) = sin(x) / (1-cos(x))
Prove tan(x) sin(x) + cos(x) = sec(x)
Prove (1 / tan(x)) + tan(x) = 1 / (sin(x) × cos(x))
Prove sin(x) - sin(x) × cos²(x) = sin³(x)
Prove cos(x) / (1 + sin(x)) + (1 + sin(x)) / cos(x) = 2 sec(x)
Prove cos(x) / (1 - sin(x)) - cos(x) / (1 + sin(x)) = 2 tan(x)
Prove (1 - sin(x)) / cos(x) = cos(x) / (1 + sin(x))
Prove cos²(x) = (csc(x) cos(x)) / (tan(x) + cot(x))

Prove (sin⁴(x) - cos⁴(x)) / (sin²(x) - cos²(x)) = 1
Prove tan²(x) / (tan²(x) + 1) = sin²(x)
Prove 1 - 2cos²(x) = (tan²(x) - 1) / (tan²(x) + 1)
Prove tan²(x) = csc²(x) tan²(x) - 1
Prove sec(x) + tan(x) = cos(x) / (1 - sin(x))
Prove (csc(x) / sin(x)) - (cot(x) / tan(x)) = 1
Prove sin⁴(x) - cos⁴(x) = 1 - 2cos²(x)
Prove (sin(x) - cos(x))² + (sin(x) + cos(x))² = 2
Prove (sin²(x) + 4sin(x) + 3) / cos²(x) = (3 + sin(x)) / (1 - sin(x))
Prove (cos(x) / (1 - sin(x))) - tan(x) = sec(x)
Prove tan²(x) + 1 + tan(x) sec(x) = (1 + sin(x)) / cos²(x)

Proving a trigonometric identity simply means demonstrating that the two equations really are equivalent. Click on the individual trig equations to get the identities proof demonstration.