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NDA 2017 Maths · Mathematics · Trigonometric Functions and Identities · hard

The value of tan 9^°-tan 27^°-tan 63^°+tan 81^° is

Single correct option

The value of tan⁡9∘−tan⁡27∘−tan⁡63∘+tan⁡81∘\tan9^\circ-\tan27^\circ-\tan63^\circ+\tan81^\circ is
  1. A. 22
  2. B. 00
  3. C. 88
  4. D. 44
Show answer and solution

Answer: (D) 44

Since tan⁡81∘=cot⁡9∘\tan81^\circ=\cot9^\circ and tan⁡63∘=cot⁡27∘\tan63^\circ=\cot27^\circ, the expression is (tan⁡9∘+cot⁡9∘)−(tan⁡27∘+cot⁡27∘)=2sin⁡18∘−2sin⁡54∘(\tan9^\circ+\cot9^\circ)-(\tan27^\circ+\cot27^\circ)=\frac{2}{\sin18^\circ}-\frac{2}{\sin54^\circ}. With sin⁡18∘=5−14\sin18^\circ=\frac{\sqrt5-1}4, sin⁡54∘=5+14\sin54^\circ=\frac{\sqrt5+1}4 this is 85−1−85+1=164=4\frac{8}{\sqrt5-1}-\frac{8}{\sqrt5+1}=\frac{16}{4}=4.
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Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake