Prove each of the following identities
l—tana _ cota-l
t-s. 'st‘9-stfa - (aroz-. <trt= <
elf’ D 4» yr“
<3?/ J 5rn°<
C0ﬁ(( _ ‘*"“(‘°’%T—)
Even and Odd Identities
sin(-x) = -sin(x) cos(-x) = cos(x) tan(—x) = -tan(x)
The sine and tangent functions are ODD functions. Cosine is an EVEN function.
Some Strategies for Proving Trigonometric Identities
(1) Work with the more complicated side of the identity first.
(2) Rewrite both sides of the identity exclusively in terms of sine and cosine.
(3) Use a Pythagorean identity to make an appropriate substitution.
(4) Simplify complex fractions or rewrite fractions sums or differences with a
(5) Use factoring (especially differences of squares).
All of the above are just suggestions or "rules of thumb. "
F eel free to disregard any or all of the above at any time.
The Sam and Difference Identities
_. =/*sin(a + B) = sinaeosﬁ+ cosasin/3
Sin(a _ I3) = Sin (1 cosﬁ — Cos a Sin ﬂ Notice the patterns and get ready
___y; oS(a+ = cos acos ﬂ _ sina sinﬁ I0 dance . .. UH. ’ Sit! !! Dance!
cos a-13) = cosacos/3+sinasinﬂ
11/ [AGES cosINE