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