CBSE
2026
Class Class 10 · Mathematics
1 Marks · Mcq
✅ Verified
$\dfrac{\sec^2 A-1}{\sin^2 A}$ is same as
A. $\cos^2 A$
B. $\sec^2 A$
C. $-\sec^2 A$
D. $\cot^2 A$
✅ Answer & Solution
✅ Correct Answer: B
Step 1: Use the identity $\sec^2 A-1=\tan^2 A$.
Step 2: $$\frac{\sec^2A-1}{\sin^2A}=\frac{\tan^2A}{\sin^2A}$$
Step 3: Write $\tan^2A=\dfrac{\sin^2A}{\cos^2A}$:
$$=\frac{\sin^2A}{\cos^2A}\times\frac{1}{\sin^2A}=\frac{1}{\cos^2A}$$
Step 4: $\dfrac{1}{\cos^2A}=\sec^2A$.
Answer: (B)
✅ Verified by Super Admin
