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AP EAMCET · Maths · Trigonometric Ratios & Identities

Match the items of List - I with those of the entires of List - II
\(List - I\)
\(\begin{aligned} & \text { (I) } \sin ^2 5^{\circ}+\sin ^2 10^{\circ}+ \\ & \sin ^2 15^{\circ}+\ldots+\sin ^2 90^{\circ}=\end{aligned}\)
\(\begin{aligned} & \text { (II) } \tan ^2 5^{\circ} \cdot \tan ^2 10^{\circ} \text {. } \\ & \tan ^2 15^{\circ} \ldots \tan ^2 85^{\circ}= \\ & \end{aligned}\)
\(\begin{aligned} & \text { (III) } \cos ^2 5^{\circ}+\cos ^2 10^{\circ} \\ & +\cos ^2 15^{\circ}+\ldots+\cos ^2 180^{\circ}=\end{aligned}\)
\(\begin{gathered}\text { (IV) } \cot 5^{\circ}+\cot 10^{\circ}+\cot 15^{\circ} \\ +\ldots .+\cot 175^{\circ}=\end{gathered}\)
\(List - II\)
(A) \(0\)
(B) \(\frac{19}{2}\)
(C) \(18\)
(D) \(1\)
(E) \(-1\)

  1. A (I) - (B), (II) - (D), (III) - (C), (IV) - (A)
  2. B (I) - (B), (II) - (E), (III) - (A), (IV) - (C)
  3. C (I) - (B), (II) - (C), (III) - (A), (IV) - (D)
  4. D (I) - (C), (II) - (B), (III) - (D), (IV) - (E)
Verified Solution

Answer & Solution

Correct Answer

(A) (I) - (B), (II) - (D), (III) - (C), (IV) - (A)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { } \begin{array}{l} \text { (I) } \sin ^2 5^{\circ}+\sin ^2 10^{\circ}+\sin ^2 15^{\circ}+\ldots+\sin ^2 90^{\circ} \\ =\sin ^2 90^{\circ}+\left(\sin ^2 5^{\circ}+\sin ^2 85^{\circ}\right)+\left(\sin ^2 10^{\circ}+\sin ^2 80^{\circ}\right)+ \\ \left(\sin…