Let 0

Question

Let 0<θ_1<θ_2<θ_3<… denotes the positive solutions of the equation 3+3cos⁡θ=2sin^2⁡θ. If θ_3+θ_7=aπ, where a is an integer, then the value of a is equal to

MARKS Content Team · Accepted Answer

Correct answer: (A) 6. 3+3cos⁡θ=2sin^2⁡θ=2-2cos^2⁡θ. ⇒2cos^2⁡θ+3cos⁡θ+1=0 ⇒cos⁡θ=-1,-1/2 ⇒θ=2n+1π or 2nπ±(2π)/3 ⇒θ=(2π)/3,π,(4π)/3,(8π)/3,3π,(10π)/3,(14π)/3,5π i.e. θ_3+θ_7=(4π)/3+(14π)/3=(18π)/3=6π ⇒a=6

Let $0 < θ_{1} < θ_{2} < θ_{3} < \dots$ denotes the positive solutions of the equation $3 + 3 \cos θ = 2 \sin^{2} θ$ . If $θ_{3} + θ_{7} = a π$ , where $a$ is an integer, then the value of $a$ is equal to

Solution

More Trigonometric Equations Questions

Let 0<θ1<θ2<θ3<… denotes the positive solutions of the equation 3+3cos⁡θ=2sin2⁡θ. If θ3+θ7=aπ, where a is an integer, then the value of a is equal to

Solution

More Trigonometric Equations Questions

Let $0 < θ_{1} < θ_{2} < θ_{3} < \dots$ denotes the positive solutions of the equation $3 + 3 \cos θ = 2 \sin^{2} θ$ . If $θ_{3} + θ_{7} = a π$ , where $a$ is an integer, then the value of $a$ is equal to