Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2024 · Mathematics · Trigonometric Ratios & Identities

What is the value of 65^ ^ +2 45^ ^ -2 40^ ^ - 25^ ^ ?

What is the value of tan⁡65∘+2tan⁡45∘−2tan⁡40∘−tan⁡25∘?\tan 65^{{}^{\circ}}+2 \tan 45^{{}^{\circ}}-2 \tan40^{{}^{\circ}}-\tan 25^{{}^{\circ}} ?

Options

  1. A0
  2. B1
  3. C2
  4. D4

Correct answer

C. 2

Step-by-step solution

tan⁡(90−25)∘+2−2tan⁡40∘−tan⁡25∘\tan (90-25)^{{}^{\circ}}+2-2 \tan 40^{{}^{\circ}}-\tan 25^{{}^{\circ}}=cot⁡25∘−tan⁡25∘−2tan⁡40∘+2=cos⁡25∘sin⁡25∘−sin⁡25∘cos⁡25∘−2tan⁡40∘+2=cos⁡225∘−sin⁡225∘sin⁡25∘⋅cos⁡25∘−2tan⁡40∘+2=cos⁡2(25∘)sin⁡25∘⋅cos⁡25∘−2tan⁡40∘+2=2×cos⁡50∘2sin⁡25∘⋅cos⁡25∘−2tan⁡40∘+2=2cos⁡50∘sin⁡50∘−2tan⁡40∘+2=2cot⁡50∘−2tan⁡40∘+2=2tan⁡40∘−2tan⁡40∘+2=2.\begin{aligned} & =\cot 25^{{}^{\circ}}-\tan 25^{{}^{\circ}}-2 \tan 40^{{}^{\circ}}+2 \\ & =\frac{\cos 25^{{}^{\circ}}}{\sin 25^{{}^{\circ}}}-\frac{\sin 25^{{}^{\circ}}}{\cos 25^{{}^{\circ}}}-2 \tan 40^{{}^{\circ}}+2 \\ & =\frac{\cos ^2 25^{{}^{\circ}}-\sin ^2 25^{{}^{\circ}}}{\sin 25^{{}^{\circ}} \cdot \cos 25^{{}^{\circ}}}-2 \tan 40^{{}^{\circ}}+2 \\ & =\frac{\cos 2\left(25^{{}^{\circ}}\right)}{\sin 25^{{}^{\circ}} \cdot \cos 25^{{}^{\circ}}}-2 \tan 40^{{}^{\circ}}+2 \\ & =\frac{2 \times \cos 50^{{}^{\circ}}}{2 \sin 25^{{}^{\circ}} \cdot \cos 25^{{}^{\circ}}}-2 \tan 40^{{}^{\circ}}+2 \\ & =\frac{2 \cos 50^{{}^{\circ}}}{\sin 50^{{}^{\circ}}}-2 \tan 40^{{}^{\circ}}+2 \\ & =2 \cot 50^{{}^{\circ}}-2 \tan 40^{{}^{\circ}}+2 \\ & =2 \tan 40^{{}^{\circ}}-2 \tan 40^{{}^{\circ}}+2=2.\end{aligned}$$
Practice Trigonometric Ratios & Identities on Quantrex Academy →

More from Trigonometric Ratios & Identities

If θ lies in the fourth quadrant and 3 θ+4=0 , then what is the value of 2θ+ 2θ ? NDA 2026If α+ β=0= α+ β , α≠β then what is a value of 2α+ 2β+2 (α+β) ? NDA 2026If 2 4β= 2α+ 2α , then which one of the following is a possible value of (α+β) ? NDA 2026If x= θ- θ and y= θ+ θ , then which one of the following is correct ? NDA 2026If θ=(1)/(3) , then what is the value of ((θ)/(2)) ((3θ)/(2)) ? NDA 2026If A and B are acute angles such that 2A+2B=π , then what is the maximum value of A· B ? NDA 2026x+ 3 x is maximum when x is equal to NDA 2026In a triangle ABC , A= B+ C then what is ((B)/(2))+ ((B)/(2))equal to ? NDA 2026If α and β are complementary angles such that α-β=(π)/(6) and m β=n α , then what is… NDA 2026For the following two (02) items: Let A + B = p and A + B = q . What is (p^2 - q^2)/(p^2… NDA 2025For the following two (02) items: Let p = cosec\, 20° and q = cosec\, 70° . What is (p^2… NDA 2025For the following two (02) items: Let A + B = p and A + B = q . What is (p)/(q) equal to? NDA 2025For the following two (02) items: Let p = cosec\, 20° and q = cosec\, 70° . What is ( 3… NDA 2025Consider the following for the three (03) items that follow: Let p = 35° , q = 25° and r… NDA 2025Consider the following for the three (03) items that follow: Let p = 35° , q = 25° and r… NDA 2025Consider the following for the three (03) items that follow: Let p = 35° , q = 25° and r… NDA 2025 Full Trigonometric Ratios & Identities list Trigonometric Ratios & Identities JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs