If θ_1 and θ_2 be respectively the smallest and the largest values of θ in 0,2π-π which satisfy the equation, 2cot^2⁡θ-5/(sin⁡θ)+4=0 , then…

Question

If θ_1 and θ_2 be respectively the smallest and the largest values of θ in 0,2π-π which satisfy the equation, 2cot^2⁡θ-5/(sin⁡θ)+4=0 , then ∫θ_1θ_2cos^2⁡3θdθ is equal to:

MARKS Content Team · Accepted Answer

Correct answer: (A) (π)/3. 2cot^2⁡θ-5/(sin⁡θ)+4=0 (2cos^2⁡θ)/(sin^2⁡θ)-5/(sin⁡θ)+4=0 2cos^2⁡θ-5sin⁡θ+4sin^2⁡θ=0, sin⁡θ≠0 2sin^2⁡θ-5sin⁡θ+2=0 2sin⁡θ-1sin⁡θ-2=0 sin⁡θ=1/2 θ=(π)/6,(5π)/6; θ∈0,2π-π ∴∫π/65π/6cos^2⁡3θdθ=∫π/65π/6(1+cos⁡6θ)/2dθ =1/2θ+(sin⁡6θ)/6x/65π/6=1/2(5π)/6-(π)/6+1/60-0=1/2.(4π)/6=(π)/3

If $θ_{1}$ and $θ_{2}$ be respectively the smallest and the largest values of $θ$ in $(0, 2 π) - \{π\}$ which satisfy the equation, $2 \cot^{2} θ - \frac{5}{\sin θ} + 4 = 0$ , then $\int_{θ_{1}}^{θ_{2}} \cos^{2} 3 θ d θ$ is equal to:

Solution

Relevant Questions

If θ1 and θ2 be respectively the smallest and the largest values of θ in 0,2π-π which satisfy the equation, 2cot2⁡θ-5sin⁡θ+4=0 , then ∫θ1θ2cos2⁡3θdθ is equal to:

Solution

Relevant Questions

If $θ_{1}$ and $θ_{2}$ be respectively the smallest and the largest values of $θ$ in $(0, 2 π) - \{π\}$ which satisfy the equation, $2 \cot^{2} θ - \frac{5}{\sin θ} + 4 = 0$ , then $\int_{θ_{1}}^{θ_{2}} \cos^{2} 3 θ d θ$ is equal to: