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JEE Main 202523 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
23 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

JEE Main 2025 · 23 January · Morning Shift · Mathematics · Trigonometric Ratios & Identities

The value of ( 70^ ) ( 10^ 70^ -1) is

The value of (sin⁡70∘)(cot⁡10∘cot⁡70∘−1)is\left(\sin 70^{\circ}\right) \left(\cot 10^{\circ} \cot 70^{\circ}-1\right) is

Options

  1. A2/32 / 3
  2. B11
  3. C00
  4. D3/23 / 2

Correct answer

B. 11

Step-by-step solution

(sin⁡70∘)(cot⁡10∘cot⁡70∘−1)=sin⁡70∘cot⁡10∘cot⁡70∘−sin⁡70∘=cot⁡10∘cos⁡70∘−sin⁡70∘=cos⁡10∘cos⁡70∘−sin⁡70∘sin⁡10∘sin⁡10∘=cos⁡(10∘+70∘)sin⁡10∘=cos⁡80∘sin⁡10∘=1\begin{aligned} & \left(\sin 70^{\circ}\right)\left(\cot 10^{\circ} \cot 70^{\circ}-1\right) \\ & =\sin 70^{\circ} \cot 10^{\circ} \cot 70^{\circ}-\sin 70^{\circ} \\ & =\cot 10^{\circ} \cos 70^{\circ}-\sin 70^{\circ} \\ & =\frac{\cos 10^{\circ} \cos 70^{\circ}-\sin 70^{\circ} \sin 10^{\circ}}{\sin 10^{\circ}} \\ & =\frac{\cos \left(10^{\circ}+70^{\circ}\right)}{\sin 10^{\circ}} \\ & =\frac{\cos 80^{\circ}}{\sin 10^{\circ}}=1\end{aligned}
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