Write the solution set of the equation 2 cos-14 cos-5-0 in the interval -0-2 -

We have, (2 cos θ+1)(4 cos θ+5)=0 ⇒ csoθ= 1/2 or cos θ = 5/4 Since cosθ ≠ 5/4 for any value of x the only solutins of the given equation in [0,2π] are x = ...

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Standard XII

Mathematics

Equations with Solutions at Boundary Values

Write the sol...

Question

$Write the solution set of the equation (2 c o s θ + 1) (4 c o s θ + 5) = 0 i n t h e i n t e r v a l [0, 2 π] .$

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Solution

$W e h a v e, (2 c o s θ + 1) (4 c o s θ + 5) = 0 \Rightarrow c s o θ = \frac{- 1}{2} o r c o s θ = \frac{- 5}{4} S i n c e c o s θ \neq \frac{- 5}{4} f o r a n y v a l u e o f x t h e o n l y s o l u t i n s o f t h e g i v e n e q u a t i o n i n [0, 2 π] a r e x = \frac{2 π}{3}, \frac{4 π}{3} .$

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Write the solution set of the equation(2 cos θ+1)(4 cos θ+5)=0 in the interval[0,2π].

We have,(2 cos θ+1)(4 cos θ+5)=0⇒csoθ=−12 or cos θ =−54Since cosθ ≠ −54 for any value of x the only solutins of the given equation in [0,2π]are x =2π3,4π3.

$Write the solution set of the equation (2 c o s θ + 1) (4 c o s θ + 5) = 0 i n t h e i n t e r v a l [0, 2 π] .$