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Express tan22.5 using cos45
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5 votes
Express tan22.5 using cos45

User Melpomene
by
6.2k points

1 Answer

3 votes
cos45 = cos(2*22.5) = (cos22.5)^2 - (sin22.5)^2 = (cos22.5)^2 * (1-(tan22.5)^2)

= (1 + cos45)/2 * (1-(tan22.5)^2)

Now, solve for tan22.5:

tan22.5 = sqrt(1 - 2cos45 / (1+cos45) )
User Vivek Salve
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6.0k points
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