If -3cos-sin-2- then general value of - is

The correct option is C nπ+( 1)^n π/4 π/3,n ∈ Z Given equation: √(3)cosθ+sinθ=√(2) ...(i) This is of form α cosθ+b sin θ=c Where a=√(3),b=1 and c=√(2) ...

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

Byju's Answer

Standard XII

Mathematics

Equations of the Form acosθ+bsinθ = c

If √3cosθ+sin...

Question

$I f \sqrt{3} c o s θ + s i n θ = \sqrt{2}, t h e n g e n e r a l v a l u e o f θ i s$

$n π + (- 1)^{n} \frac{π}{4}, n \in Z$

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

$(- 1)^{n} \frac{π}{4} - \frac{π}{3}, n \in Z$

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

$n π + \frac{π}{4} - \frac{π}{3}, n \in Z$

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

$n π + (- 1)^{n} \frac{π}{4} - \frac{π}{3}, n \in Z$

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

Open in App

Solution

The correct option is D
$n π + (- 1)^{n} \frac{π}{4} - \frac{π}{3}, n \in Z$

$G i v e n e q u a t i o n : \sqrt{3} c o s θ + s i n θ = \sqrt{2} . . . (i) T h i s i s o f f o r m α c o s θ + b s i n θ = c W h e r e a = \sqrt{3}, b = 1 a n d c = \sqrt{2} L e t : a = r s i n α a n d b = r c o s α . N o w, r = \sqrt{a^{2} + b^{2}} = \sqrt{{(\sqrt{3})}^{2}} + 1^{2} = 2 A n d, t a n α = \frac{a}{b} \Rightarrow t a n a l p h a = \frac{\sqrt{3}}{1} \Rightarrow t a n α = t a n \frac{π}{3} \Rightarrow α = \frac{π}{3} P u t t i n g a = \sqrt{3} = r s i n α a n d b = 1 = r c o s α i n e q u a t i o n (i), w e g e t : r c o s θ s i n α + r s i n θ c o s α = \sqrt{2} \Rightarrow r s i n (θ + α) = \sqrt{2} \Rightarrow 2 s i n (θ + α) = \sqrt{2} \Rightarrow s i n (θ + \frac{π}{3}) = \frac{1}{\sqrt{2}} \Rightarrow s i n (θ + \frac{π}{3}) = c o s \frac{π}{4} \Rightarrow θ + \frac{π}{3} = n π + (- 1)^{n} \frac{π}{4}, n \in Z \Rightarrow θ = n π + (- 1)^{n} \frac{π}{4} - \frac{π}{3}, n \in Z$

Suggest Corrections

If √3 cosθ+sinθ=√2,then general value of θ is

$I f \sqrt{3} c o s θ + s i n θ = \sqrt{2}, t h e n g e n e r a l v a l u e o f θ i s$