If 2cos2θ + 3sinθ = 3, where 0° < θ < 90°, then what is the value of sin22θ + cos2θ + tan22θ + cosec22θ?
A. $$\frac{{29}}{6}$$
B. $$\frac{{29}}{3}$$
C. $$\frac{{35}}{6}$$
D. $$\frac{{35}}{{12}}$$
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & 2{\cos ^2}\theta + 3\sin \theta = 3 \cr & {\text{Let }}\theta = {30^ \circ } \cr & 2{\cos ^2}{30^ \circ } + 3\sin {30^ \circ } = 3 \cr & 2 \times \frac{3}{4} + 3 \times \frac{1}{2} = 3 \cr & 3 = 3 \cr & {\sin ^2}2\theta + {\cos ^2}\theta + {\tan ^2}2\theta + {\text{cose}}{{\text{c}}^2}2\theta \cr & = {\sin ^2}{60^ \circ } + {\cos ^2}{30^ \circ } + {\tan ^2}{60^ \circ } + {\text{cose}}{{\text{c}}^2}{60^ \circ } \cr & = \frac{3}{4} + \frac{3}{4} + 3 + \frac{4}{3} \cr & = \frac{3}{2} + 3 + \frac{4}{3} \cr & = \frac{{9 + 18 + 8}}{6} \cr & = \frac{{35}}{6} \cr} $$Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
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