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If sec theta = 2,find 4 cos theta-root 3 sin theta/tan theta

User Kikuchiyo
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cos theta = 1 /sec theta so cos theta = 1/2

and 4 cos theta = 4 * 1/2 = 2

sin theta = sqrt ( 1 - cos^2 theta) = sqrt 1 - 1/4) = sqrt (3/4) = sqrt3/2

root 3 sin theta = 3/2

tan theta = sin theta / cos theta = sqrt3 / 2 / 1/2 = 2*sqrt3/ 2 = sqrt3

so the answer is 2 - 3/2 / sqrt3 = 1/2 / sqrt3 = sqrt3 / 6
User TFischer
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