Write the number of sulutions of the equation tan x- x-2 cos x in the interval -0-2 -

Tan x+ sec x=2 cos x 1+sin x=2 cos^2 x 2(1 sin^2 x)=1+sin x 2 sin^2 x+sin x 1=0 (2 sin x 1)(sin x+1=0) sin x=1/2 Or 1 x=π/6,5π/6,3π/2 Thus,there are 3 so ...

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Standard XII

Mathematics

Equations with Solutions at Boundary Values

Write the num...

Question

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

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Solution

$t a n x + s e c x = 2 c o s x 1 + s i n x = 2 c o s^{2} x 2 (1 - s i n^{2} x) = 1 + s i n x 2 s i n^{2} x + s i n x - 1 = 0 (2 s i n x - 1) (s i n x + 1 = 0) s i n x = \frac{1}{2} O r - 1 x = \frac{π}{6}, \frac{5 π}{6}, \frac{3 π}{2} Thus,there are 3 solutions in interval [0, 2 π] .$

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

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

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

$t a n x + s e c x = 2 c o s x 1 + s i n x = 2 c o s^{2} x 2 (1 - s i n^{2} x) = 1 + s i n x 2 s i n^{2} x + s i n x - 1 = 0 (2 s i n x - 1) (s i n x + 1 = 0) s i n x = \frac{1}{2} O r - 1 x = \frac{π}{6}, \frac{5 π}{6}, \frac{3 π}{2} Thus,there are 3 solutions in interval [0, 2 π] .$