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Recall:Compare factoring x2+2x+1To factoring x2-2x+1Factor x2-1Evaluate 13+14Evaluate 255Why can’t you just cancel the fives out in this expression 5+65 ?Rewrite so there is no radical in the denominator 21+3Trig Equation eg. sinθ=0.6789Trig Identity eg. sin2θ+cos2θ=1What is the difference between a trig equation and a trig identity?The following trig identities are important to know. They can be used to prove more complicated trig identities.Reciprocal IdentitiesQuotient IdentitiesPythagorean IdentitiesTo prove a trig identity, you must show that each side of the identity is equivalent.Some Suggestions….Start with the most complicated side and work on it until it looks like the other side or work on both sides until they look identical.Rewrite all trig ratios in terms of sine and cosine.If there are fractions, try a common denominator.Try factoring and cancelling. *Difference of Squares often appears! Example 1Prove that 1+cot2θ=csc2θ. (Pretend you don’t know the Pythagorean Identities) Example 2 Prove that. tanθ= sinθ+sin2θcosθ1+sinθExample 3Prove that sin2θ1-cosθ =1+cosθExample 4Prove that 1-sin2θ=sinθcosθcotθExample 5Prove that cosθ1-sinθ+cosθ1+sinθ = 2cosθExample 6Prove that tanθ+cotθ= secθsinθExample 7 Prove that cot2θ1+tan2θ=cscθTrig Identity WorksheetPart AProve the following identities. Each question has different tricks – you must complete all of them!2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) Part BDetermine which of the following are identities using a graphing calculator or geogebra.28) 29) 30) ................
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