1 tan 1 sin(2 ) Prove: . 1 tan cos(2 ) Start with: 1 tan 1 tan sin cos sin
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Trigonometry, Mckeague, 6th edition Homework Proof 5.3 #53 Prove: 1 tan x 1 tan x Start with: 1 tan x 1 tan x sin x 1 cos x sin x 1 cos x cos x sin x cos x cos x sin x cos x sin x 1 sin(2 x) . cos(2 x) cos x sin x cos x cos x cos x sin x cos x cos x cos x cos x sin x cos x sin x cos x cos x sin x cos x Now this is a problem. I don't have any identities to use here. I need squares to get some possiblities for identities. One way to make squres is multiple by the conjugate. cos x sin x cos x sin x cos x sin x cos x sin x cos 2 x 2sin x cos x sin 2 x cos 2 x sin 2 x 1 2sin x cos x . cos(2 x) Therefore, 1 tan x 1 tan x The "fancy one" keeps the expression equivalent still. The result of FOILing. Note all the squares and identities. 1 sin(2 x) . cos(2 x)
