SOLUTION: Show that (a) (tanx - cosx)/sinxcosx = sec²x - cosec²x (b) sin⁴x + cos⁴x = 1- 2sin²xcos²x

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Question 1132184: Show that
(a) (tanx - cosx)/sinxcosx = sec²x - cosec²x
(b) sin⁴x + cos⁴x = 1- 2sin²xcos²x
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
(a)



start with



=

=

=

=

=

==>this is your solution, it’s not (you probably made mistake while typing)


(b)



start with



=

=

=

=

=




Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
.

            I will solve the part  (b)  here only,  in a shorter way. 


Start with


     +  = 1.


Square both sides


     +  +  = 1


Move the term    from the left side to the right, changing the sign


     +  = 1 - .

QED.


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