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. Examples2x = 53 x = ±5 cos x = -1 x = π, 3 π, 5 π …

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 = 5x 2 +30x +45 sin x sec x = tan x

Guidelines Work 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 that sec 2 Ѳ -1 = sin 2 Ѳ sec 2 Ѳ

Verify that = 2 sec 2 Ѳ 1– sin Ѳ 1 + sin Ѳ

Verify that (tan 2 Ѳ +1)(cos 2 Ѳ – 1) = -tan 2 Ѳ

Verify that tan Ѳ + cot Ѳ = secѲcscѲ

Verify that cot 2 Ѳ = 1 – sinѲ 1 + cscѲ sin Ѳ