The number of solutions to tan x -sec x -2 cos x in 0- 2- is

The given equations is tan x +sec x =2 cos x ⇒ sin x+1 =2 cos^2 x ⇒ sin x+1 =2(1 sin^2 x) ⇒ 2 sin^2 x+sin x 1 =0 ⇒ (2 sin x 1)(sin x+1)=0 ⇒ sin x =1/2, 1 ⇒ x ...

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Standard XII

Mathematics

Solving Simultaneous Trigonometric Equations

The number of...

Question

The number of solutions to tan x +sec x =2 cos x in $(0, 2 π)$ is

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Solution

The correct option is B 3
The given equations is
tan x +sec x =2 cos x
$\Rightarrow s i n x + 1 = 2 c o s^{2} x \Rightarrow s i n x + 1 = 2 (1 - s i n^{2} x) \Rightarrow 2 s i n^{2} x + s i n x - 1 = 0 \Rightarrow (2 s i n x - 1) (s i n x + 1) = 0 \Rightarrow s i n x = \frac{1}{2}, - 1 \Rightarrow x = 30^{\circ}, 150^{\circ}, 270^{\circ}$

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The number of solutions to tan x +sec x =2 cos x in (0,2π) is

The correct option is B 3The given equations is tan x +sec x =2 cos x ⇒sinx+1=2cos2x⇒sinx+1=2(1−sin2x)⇒2sin2x+sinx−1=0⇒(2sinx−1)(sinx+1)=0⇒sinx=12,−1⇒x=30∘,150∘,270∘

The number of solutions to tan x +sec x =2 cos x in $(0, 2 π)$ is