If 2 sin 2-3 cos- where 0 - 2 - then find the value of -

2sin^2θ=3 cosθ 2(1 cos^2θ)=3 cosθ [∵ sin^2θ=1 cos^2θ] 2 2 cos^2θ=3 cos θ ⇒ 2 cos^2θ+3 cos θ 2=0 ⇒ 2 cos^2θ+4 cos θ cosθ 2=0 ⇒ 2 cos θ[cosθ+2] [cosθ+ ...

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

Byju's Answer

Standard XII

Mathematics

Equations with Solutions at Boundary Values

If 2 sin 2θ=3...

Question

$I f 2 s i n^{2} θ = 3 c o s θ, w h e r e 0 \leq θ \leq 2 π, t h e n f i n d t h e v a l u e o f θ .$

Open in App

Solution

$2 s i n^{2} θ = 3 c o s θ 2 (1 - c o s^{2} θ) = 3 c o s θ [∵ s i n^{2} θ = 1 - c o s^{2} θ] 2 - 2 c o s^{2} θ = 3 c o s θ \Rightarrow 2 c o s^{2} θ + 3 c o s θ - 2 = 0 \Rightarrow 2 c o s^{2} θ + 4 c o s θ - c o s θ - 2 = 0 \Rightarrow 2 c o s θ [c o s θ + 2] - [c o s θ + 2] = 0 \Rightarrow (2 c o s θ - 1) (c o s θ + 2) = 0 \Rightarrow 2 c o s θ - 1 = 0 o r c o s θ = - 2 ∵ θ = \frac{π}{3,} \frac{5 π}{3}$

Suggest Corrections

Similar questions

Q. Solve the following equation

2 {sin}^{2} θ = 3 cos θ

in the interval

0 \leq θ \leq 2 π

Q. If

0 < θ < 2 π,

then the intervals of values of

θ

for which

2 {sin}^{2} θ - 5 sin θ + 2 > 0,

Q. If

2 \sin^{2} θ - \cos^{2} θ = 2

, then find the value of

θ

Q. Solve the following equations:

(i)

\cot θ + \tan θ = 2

[NCERT EXEMPLAR]
(ii)

2 \sin^{2} θ = 3 \cos θ, 0 \leq θ \leq 2 π

[NCERT EXEMPLAR]
(iii)

\sec θ \cos 5 θ + 1 = 0, 0 < θ < \frac{π}{2}

[NCERT EXEMPLAR]
(iv)

5 \cos^{2} θ + 7 \sin^{2} θ - 6 = 0

[NCERT EXEMPLAR]
(v)

\sin x - 3 \sin 2 x + \sin 3 x = \cos x - 3 \cos 2 x + \cos 3 x

[NCERT EXEMPLAR]

Q. If

0 < θ < 90

and

2 sin 2 θ = \sqrt{3},

then find the value of

θ .

Join BYJU'S Learning Program

If 2sin2θ=3 cosθ,where 0≤θ≤ 2π,then find the value of θ.

2sin2θ=3 cosθ2(1−cos2θ)=3 cosθ [∵sin2θ=1−cos2θ]2−2 cos2θ=3 cos θ⇒2 cos2θ+3 cos θ−2=0⇒2 cos2θ+4 cos θ−cosθ−2=0⇒2 cos θ[cosθ+2]−[cosθ+2]=0⇒(2 cos θ−1)(cos θ+2)=0⇒2 cos θ −1=0 or cosθ=−2∵ θ=π3,5π3

$I f 2 s i n^{2} θ = 3 c o s θ, w h e r e 0 \leq θ \leq 2 π, t h e n f i n d t h e v a l u e o f θ .$