Choose the correct alternative answer for the following questions. 1 + tan2θ = ? (A) cot2θ (B) cosec2θ (C) sec2θ (D) tan2θ

Solution $$\text{The correct answer is (A) } \frac{1}{\sqrt{2}}.$$ We know that $$\csc\theta = \frac{1}{\sin\theta}$$. Therefore, $$\csc 45^\circ = \frac{1}{\sin 45^\circ} = \frac{1}{\frac{1}{\sqrt{2}}} = \frac{\sqrt{2}}{1} = \sqrt{2}$$. So, option (B) $$\sqrt{2}$$ is incorrect. The correct answer is (A) $$\frac{1}{\sqrt{2}}$$.