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Question

Write the number of sulutions of the equation tan x +sec x = 2 cos x in the interval [0,2π].


Solution

tan x+ sec x=2 cos x1+sin x=2 cos2 x2(1sin2 x)=1+sin x2 sin2 x+sin x1=0(2 sin x1)(sin x+1=0)sin x=12 Or1x=π6,5π6,3π2Thus,there are 3 solutions in interval[0,2π].

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