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

The correct option is B 3The 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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

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

Suggest Corrections

Similar questions

Q. The number of solutions of

tan x + sec x = 2 cos x

[0, 2 π]

Q. Number of solutions of the equation

t a n x + s e c x = 2 c o s x

lying in the interval

[0, 2 π]

Q. Number of solutions of

tan x + sec x = 2 cos x

in intarval

[0, 2 π]

Q. The number of solutions of the equation

tan x + sec x = 2 cos x

in the interval

[0, 2 π]

Q. Number of solutions of the equations tan x + sec x=2 cos x lying in the interval

[0, 2 π]

Join BYJU'S Learning Program

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