If $${\text{co}}{{\text{s}}^4}\theta - {\sin ^4}\theta = \frac{2}{3},$$ then the value of $${\text{1}} - {\text{2}}{\sin ^2}\theta $$ is?
A. $$\frac{4}{3}$$
B. 0
C. $$\frac{2}{3}$$
D. $$\frac{1}{3}$$
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\text{co}}{{\text{s}}^4}\theta - {\sin ^4}\theta = \frac{2}{3} \cr & \Rightarrow \left( {{\text{co}}{{\text{s}}^2}\theta - {{\sin }^2}\theta } \right)\left( {{\text{co}}{{\text{s}}^2}\theta + {{\sin }^2}\theta } \right) = \frac{2}{3} \cr & \Rightarrow {\text{co}}{{\text{s}}^2}\theta - {\sin ^2}\theta = \frac{2}{3} \cr & \Rightarrow 1 - {\sin ^2}\theta - {\sin ^2}\theta = \frac{2}{3} \cr & \Rightarrow 1 - 2{\sin ^2}\theta = \frac{2}{3} \cr} $$Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
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