A value of θ lying between θ$$=0$$ and θ$$=$$π$$/2$$ and satisfying the $$equation1+sin2$$⁡θ$$cos2$$⁡θ$$4sin$$⁡$$4$$θ$$sin2$$⁡θ$$1+cos2$$⁡θ$$4sin$$⁡$$4$$θ$$sin2$$⁡θ$$cos2$$⁡θ$$1+4sin$$⁡$$4$$θ$$=0$$ is

Question

A value of θ lying between θ$$=0$$ and θ$$=$$π$$/2$$ and satisfying the $$equation1+sin2$$⁡θ$$cos2$$⁡θ$$4sin$$⁡$$4$$θ$$sin2$$⁡θ$$1+cos2$$⁡θ$$4sin$$⁡$$4$$θ$$sin2$$⁡θ$$cos2$$⁡θ$$1+4sin$$⁡$$4$$θ$$=0$$ is

Infinity Learn · Accepted Answer

Applying $$R1$$→$$R1$$−$$R3$$,$$R2$$→$$R2$$−$$R3$$ to the given determinant we $$get10$$−$$101$$−$$1sin2$$⁡θ$$cos2$$⁡θ$$1+4sin$$⁡$$4$$θ$$=0$$⇒$$1+4sin$$⁡$$4$$θ$$+cos2$$⁡θ$$+sin2$$⁡θ$$=0$$⇒$$sin$$⁡$$4$$θ$$=$$−$$1/2$$⇒$$4$$θ$$=$$π$$+$$π$$/6$$ or $$2$$π−π$$/6$$ [∵$$0$$<$$4$$θ<$$2$$π]⇒ θ$$=7$$π$$/24$$ or  $$11$$π$$/24$$

A value of $θ$ lying between $θ = 0$ and $θ = π / 2$ and satisfying the equation $|\begin{array}{ccc} 1 + \sin^{2} θ & \cos^{2} θ & 4 \sin 4 θ \\ \sin^{2} θ & 1 + \cos^{2} θ & 4 \sin 4 θ \\ \sin^{2} θ & \cos^{2} θ & 1 + 4 \sin 4 θ \end{array}| = 0$ is

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A value of θ lying between θ=0 and θ=π/2 and satisfying the equation1+sin2⁡θcos2⁡θ4sin⁡4θsin2⁡θ1+cos2⁡θ4sin⁡4θsin2⁡θcos2⁡θ1+4sin⁡4θ=0 is

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A value of $θ$ lying between $θ = 0$ and $θ = π / 2$ and satisfying the equation $|\begin{array}{ccc} 1 + \sin^{2} θ & \cos^{2} θ & 4 \sin 4 θ \\ \sin^{2} θ & 1 + \cos^{2} θ & 4 \sin 4 θ \\ \sin^{2} θ & \cos^{2} θ & 1 + 4 \sin 4 θ \end{array}| = 0$ is