A) 0
B) 1
C) 3
D) 4
Correct Answer: A
Solution :
The given equation can be written as -\[2\,{{\tan }^{2}}x+{{\tan }^{4}}x+{{\tan }^{4}}x\] \[-2{{\sec }^{2}}x\,{{\tan }^{2}}x-3=0\] \[\Rightarrow \] \[2\,{{\tan }^{2}}x+{{({{\sec }^{2}}x-1)}^{2}}+{{\tan }^{4}}x\] \[-2\,{{\sec }^{2}}x\,{{\tan }^{2}}x-3=0\] \[\Rightarrow \] \[2\,{{\tan }^{2}}x+{{\sec }^{4}}x+1-2\,{{\sec }^{2}}x\] \[+{{\tan }^{4}}x-2\,{{\sec }^{2}}x\,{{\tan }^{2}}x-3=0\] \[\Rightarrow \] \[{{({{\sec }^{2}}x-{{\tan }^{2}}x)}^{2}}=4\] \[\Rightarrow \] \[1\ne 4\] Hence, no solution exists.You need to login to perform this action.
You will be redirected in
3 sec