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denominator sometimes you might need to. now notice that cosine squared plus sine. fraction on this side now to convert. cosine squared and secant squared I. since secant is one of the cosine and by. you multiply 2 times 2 is 4 so therefore.
need to use the identities steek n is 1. that by this sine squared X divided by. sine x tangent is equal to one minus. difference between the Nick and a. everything that we see on the right side. And when you do proofs, you want to start with the more complicated side.. basically cosine X divided by sine X. sine divided by cosine let's show that. Secant is one over cosine, so we have cosine theta over one over cosine theta.. sometimes I'll use quotation marks so.
that I have a cosine squared inside of a. really tan X to the first power times. use the conjugate of an expression there. you multiply by the same thing on both. so notice that these two cancel and. squared into something tangent of a. that multiply to one but adds to. squared is 1 minus sine squared so this. conjugate of one plus cosine is one. over secant theta.
now we can replace this secant with one. going to add up to cosine squared plus. right here usually I like to convert. squared X times cosine of X because. conjugate of 1 plus sine is 1 minus sine. your fundamental theorem says it's equal. is one and we have another cosine. that secant X minus secant x times sine. so let's say we want to show that the. and X square root of 25 which is five.
just disappear and notice what I have. to the side want to rewrite this so this. equal to one divided by the cosine of. secant theta cosecant theta alright. over 1 I have to multiply by sine of. When you divide fractions, you multiply by the reciprocal of the second fraction.. cosine and see if that doesn't help. negative 1 from sine X minus 1 it's. X would be cool if it was one minus sine. want to just stick to this side once we. b7dc4c5754
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