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Class 10 › Mathematics › Introduction to Trigonometry
CBSE2026Class Class 10 · Mathematics1 Marks · Mcq✅ Verified
The value of $\left(\dfrac{1}{\sec^{2}A}+\dfrac{1}{\operatorname{cosec}^{2}A}\right)$ is :
A. more than 1
B. $1$
C. $0$
D. $-1$
✅ Answer & Solution
✅ Correct Answer: B
Step 1: Use the reciprocal relations $\dfrac{1}{\sec A}=\cos A$ and $\dfrac{1}{\operatorname{cosec} A}=\sin A$.
Step 2: Therefore
$$\frac{1}{\sec^{2}A}+\frac{1}{\operatorname{cosec}^{2}A}=\cos^{2}A+\sin^{2}A$$
Step 3: Apply the fundamental identity $\sin^{2}A+\cos^{2}A=1$.
$$=1$$
Correct option is (B) 1.
