Verifying Trigonometric Identities

Remember that a conditional equation is true for only some values in the domain. So you solve the equation by finding those values which make it true.

Examples 2x2 + 3 = 53 x = ±5

cos x = -1 x = π, 3π, 5π…

An identity is an equation that is true for all values in the domain. You simply perform algebraic steps to verify that it is true.

Examples 5(x+3)2 = 5x2 +30x +45

sin x sec x = tan x

GuidelinesWork with one side at a time. It is

often better to work with the more complicated side first.

Look for chances to factor, add fractions, FOIL, or simplify a fraction.

Look for chances to make substitutions using identities.

If you can’t do anything else, try changing all terms to sines and cosines.

And most importantly…Try something! Don’t just stare at

a problem. I often don’t know where a problem is going until I am in the middle of it. There are usually multiple ways to solve a problem.

These techniques take lots of practice and will get easier with practice!

Verify thatsec2Ѳ-1 = sin2 Ѳ sec2Ѳ

Verify that 1 + 1 = 2 sec2 Ѳ

1– sin Ѳ 1 + sin Ѳ

Verify that (tan2Ѳ +1)(cos2Ѳ – 1) = -tan2Ѳ

Verify that tan Ѳ + cot Ѳ = secѲcscѲ

Verify that cot2Ѳ = 1 – sinѲ 1 + cscѲ sin Ѳ