Name: ____________________________________________________ Date: ___________________________
Trigonometric Identities
Practice 1
Each of these expressions can be simplified to a single expression using a trig function or number or combination
thereof. Simplify each expression. Show any work.
1. sin sec 3.
xcsc
xsec
5. cos
2
(1 + tan
2
)
2.
ysec1
y cos 1
4. (tan x)(cos x)(csc x) 6. tan + cos ( ) + tan ( )
Verify each identity by showing that one side can be simplified to look like the other. Show any work.
7.
xtan
xsecxcos
= cot x 12. cos( x) sin( x) = cos x + sin x
8. tan + cot = (sec )(csc ) 13. (sin x + cos x)
2
= 1 + 2 sin x cos x
9. (tan y + cot y) sin y cos y = 1 14.
1xsec
xcotxcsc
= cot x
10.
cotcos
cscsin
=
sin1
cos
15. cos t + tan t sin t = sec t
11. (tan x + cot x)
4
= csc
4
x sec
4
x 16.
sin1
cos
= sec + tan
(HINT: simplify tanx + cotx as much as (HINT: multiply numerator and denominator by
possible by adding fractions, then do power) 1 + sin )
