1.

1). 30°2). 60°3). 45°4). 90°

Answer»

(sinθ + cosecθ) = 2.5

sinθ $(+\; \frac{1}{{{\rm{sin\theta }}}} = 2.5)$

-sin2θ + 2.5 sinθ - 1 = 0

sin2θ - 2.5sinθ + 1 = 0

sinθ $( = \frac{{ + 2.5 \PM \SQRT {6.25 - 4} }}{2})$

sinθ $( = \frac{{ + 2.5 \pm 1.5}}{2})$

∴ sinθ = 2,$(\frac{1}{2})$

sinθ = 2

∴ Not possible for 0 < θ < $(\frac{{\rm{\pi }}}{2})$

∴ sinθ = $(\frac{1}{2})$

∴ θ = 30°



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