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Simpligy 1 - tan^4 theta + sec^4 theta

label Calculus
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Oct 18th, 2017

Rewrite the problem this way.

1 + sec^4a - tan^4a   (I have written sec^4theta first and also for simplicity I am replacing theta by 'a')

=1 + (sec^2a)^2 - (tan^2a)^2  (just splitting the power 4 to squared squared)

= 1 + {(sec^2a + tan^2a)(sec^2a -tan^2a)}   using the fact that x^2-y^2 = (x+y)(x-y)

= 1+ {(sec^2a + tan^2a)(1)}      this is from a fact(trig identity) that + tan^2a = sec^2a

= 1+ sec^2a + tan^2a 

=  1+ tan^2a + sec^2a But 1+ tan^2a = sec^2a      

= 2 sec^2a = 2 sec^2theta                                       

Jan 28th, 2015

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