If θ$$1and$$ θ$$2$$ be respectively the smallest and the largest values of θ$$ln0$$,$$2$$π−πwhich satisfy the equation $$2cot2$$θ−$$5sin$$θ$$+4=0then$$ ∫θ$$1$$θ$$2cos23$$θdθis equal to:

Question

If  θ$$1and$$ θ$$2$$ be respectively the smallest and the largest values of  θ$$ln0$$,$$2$$π−πwhich satisfy the equation  $$2cot2$$θ−$$5sin$$θ$$+4=0then$$ ∫θ$$1$$θ$$2cos23$$θdθis equal to:

Infinity Learn · Accepted Answer

$$2cot2$$θ−$$5sin$$θ$$+4=0$$⇒$$2cos2$$θ$$sin2$$θ−$$5sin$$θ$$+4=0$$⇒$$2cos2$$θ−$$5sin$$θ$$+4sin2$$θ$$=0$$,$$sin$$θ≠$$0$$⇒$$2sin2$$θ−$$5sin$$θ$$+2=0$$⇒$$2sin$$θ−$$1sin$$θ−$$2=0$$⇒$$sin$$θ$$=12$$⇒θ$$=$$π$$6$$,$$5$$$$π$$$$6$$∴∫π$$/65$$π$$/6cos23$$θdθ$$=$$∫π$$/65$$π$$/61+cos6$$θ$$2d$$θ                              $$=12$$θ$$+sin6$$θ$$6$$π$$/65$$π$$/6$$ $$=125$$$$π$$$$6$$−π$$6+160$$−$$0$$ $$=12.4$$$$π$$$$6=$$π$$3$$

If $θ_{1}$ and $θ_{2}$ be respectively the smallest and the largest values of $θ \ln (0, 2 π) - \{π\}$ 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:

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If θ1and θ2 be respectively the smallest and the largest values of θln0,2π−πwhich satisfy the equation 2cot2θ−5sinθ+4=0then ∫θ1θ2cos23θdθis equal to:

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If $θ_{1}$ and $θ_{2}$ be respectively the smallest and the largest values of $θ \ln (0, 2 π) - \{π\}$ 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: