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tan x = sin x / cos x

sin x = x - (x^3/3!) + (x^5/5!) - (x^7/7!) + (x^9/9!) ... to infinity

cos x = 1 - (x^2/2!) + (x^4/4!) - (x^6/6!) + (x^8/8!) .. to infinity

tan 165 degrees = -0.267949192

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Q: How do you find the exact value of tan 165?
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tan 165/2 = 1.068691


What is the half angle formula to find the exact value for tan 165?

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cot(15)=1/tan(15) Let us find tan(15) tan(15)=tan(45-30) tan(a-b) = (tan(a)-tan(b))/(1+tan(a)tan(b)) tan(45-30)= (tan(45)-tan(30))/(1+tan(45)tan(30)) substitute tan(45)=1 and tan(30)=1/√3 into the equation. tan(45-30) = (1- 1/√3) / (1+1/√3) =(√3-1)/(√3+1) The exact value of cot(15) is the reciprocal of the above which is: (√3+1) /(√3-1)


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