10th Class Mathematics Introduction to Trigonometry Question Bank MCQs - Introduction to Trigonometry

\[\frac{1+{{\cot }^{2}}A}{1+{{\tan }^{2}}A}=\]

A) \[{{\tan }^{2}}A\]

B) \[{{\sec }^{2}}A\]

C) \[\text{cose}{{\text{c}}^{2}}A-1\]

D) \[1-{{\sin }^{2}}A\]

Correct Answer: C

Solution :

[c] \[\frac{1+{{\cot }^{2}}A}{1+{{\tan }^{2}}A}=\frac{1+{{\cot }^{2}}A}{1+\frac{1}{{{\cot }^{2}}A}}\]

\[=\frac{{{\cot }^{2}}A(1+{{\cot }^{2}}A)}{{{\cot }^{2}}A+1}={{\cot }^{2}}\cdot A=\cos e{{c}^{2}}A-1\]