Identities

Identities are used to simplify expressions. 

Pythagorean Identities  are

sin²x +cos²x=1

tan²x+1= sec²x

cot²x+1=csc²x

Reciprocal Identities are

            cscx=1/sinx              secx=1/cosx             cotx=1/tanx

Relations with negatives are

            sin(-x)=-sinx                              cos(-x)=cosx

            csc(-x)=-cscx                             sec(-x)=secx

            tan(-x)=-tanx                            cot(-x)=-cotx

Simplify.

1)  1.     (1-cosx)(1-cosx)

=1-cos²x      by using foil to multiply

=sin²x           by using Pythagorean Identities

2)  2.     sinxcosx/(1-cos²x)

= sinxcosx/sin²x      by using the Pythagorean Identities

= cosx/sinx              by cancelling a sinx from numerator and denominator

= cotx                       by the definition of cotangent

3)   3.   cos³x + cosx sin²x

= cosx(cos²x + sin²x)   by factoring cosx from each term

=cosx (1)                       by using the Pythagorean Identities

=cosx                             multiplying by 1

Love,

Jenna Roussel