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Saturday, 31 October

JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 17 March 2021, Shift 2, Maths Q82

Question 82 of 90 in this shift, Maths question 22 of 30, Section B.

Let tan⁡α\tan\alpha, tan⁡β\tan\beta and tan⁡γ\tan\gamma ; α,β,γ≠(2n−1)π2\alpha, \beta, \gamma\neq\frac{(2n-1)\pi}{2}, n∈Nn\in\mathbf{N} be the slopes of three line segments OA, OB and OC, respectively, where O is origin. If circumcentre of Δ\DeltaABC coincides with origin and its orthocentre lies on yy-axis, then the value of (cos⁡3α+cos⁡3β+cos⁡3γcos⁡αcos⁡βcos⁡γ)2\left(\frac{\cos 3\alpha+\cos 3\beta+\cos 3\gamma}{\cos\alpha\cos\beta\cos\gamma}\right)^2 is equal to __________.

Official answer

144

NTA final key.

Chapter
Trigonometric Functions
Topic
Trigonometric Identities
Idea tested
Triple Angle Formulas

Same idea in other shifts

Asked 2× in all
  1. 8 Apr 2023, Shift 2 · Q19The value of 36(4cos⁡29∘−1)(4cos⁡227∘−1)(4cos⁡281∘−1)(4cos⁡2243∘−1)36(4\cos^2 9^\circ - 1)(4\cos^2 27^\circ - 1)(4\cos^2 81^\circ - 1)(4\cos^2 243^\circ - 1) isHardSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.