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

Algebra ->  Trigonometry-basics -> SOLUTION: Show that (a) (tanx - cosx)/sinxcosx = sec²x - cosec²x (b) sin⁴x + cos⁴x = 1- 2sin²xcos²x      Log On


   

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) About Me  (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(52847) About Me  (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


    sin%5E2%28x%29 + cos%5E2%28x%29 = 1.


Square both sides


    sin%5E4%28x%29 + 2%2Asin%5E2%28x%29%2Acos%5E2%28x%29 + cos%5E4%28x%29 = 1


Move the term  2%2Asin%5E2%28x%29%2Acos%5E2%28x%29  from the left side to the right, changing the sign


    sin%5E4%28x%29 + cos%5E4%28x%29 = 1 - 2%2Asin%5E2%28x%29%2Acos%5E2%28x%29.

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.