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

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Question 1132204: Show that
(a) (tanx - cosx)/sinxcosx = sec²x - cosec²x
(b) sin⁴x + cos⁴x = 1- 2sin²xcos²x
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Show that
(a) (tanx - cosx)/sinxcosx = sec²x - cosec²x
----------
Step 1, multiply thru by sin*cos
Make an effort.
Try things.
Change to sines & cosines, eg, tan = sin/cos
Answer by ikleyn(52860)   (Show Source): You can put this solution on YOUR website!
.
            I just solved part (b) yesterday under this link

            https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1132184.html

            https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1132184.html


            For your convenience, I repeat this solution below  ONE  MORE  TIME. 


Start with


     +  = 1.


Square both sides


     +  +  = 1


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


     +  = 1 - .

QED.

Please do not post it again.


Also,  in the future,  DO  NOT  POST  more than one problem per post.

It is the  RULE,  the  REQUIREMENT  and the  POLICY  of this forum.



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