NDA 2024
Exam NDA
Year 2024
Subject Mathematics
Chapter Trigonometric Ratios & Identities NDA 2024 · Mathematics · Trigonometric Ratios & Identities
What is 17^ ^ - 17^ ^ 17^ ^ + 17^ ^ equal to?
What is \frac{\cos 17^{{}^{\circ}}-\sin 17^{{}^{\circ}}}{\cos 17^{{}^{\circ}}+\sin 17^{{}^{\circ}}}$ equal to?
Options A tan 3 4 ∘ \tan 34^{{}^{\circ}} tan 3 4 ∘ B cot 3 4 ∘ \cot 34^{{}^{\circ}} cot 3 4 ∘ C tan 6 2 ∘ \tan 62^{{}^{\circ}} tan 6 2 ∘ D cot 6 2 ∘ \cot 62^{{}^{\circ}} cot 6 2 ∘ Correct answer D. cot 6 2 ∘ \cot 62^{{}^{\circ}} cot 6 2 ∘
Step-by-step solution
Let I = cos 1 7 ∘ − sin 1 7 ∘ cos 1 7 ∘ + sin 1 7 ∘ = cos 1 7 ∘ ( 1 − sin 1 7 ∘ cos 1 7 ∘ ) cos 1 7 ∘ ( 1 + sin 1 7 ∘ cos 1 7 ∘ ) ⇒ I = tan 4 5 ∘ − tan 1 7 ∘ 1 + tan 4 5 ∘ ⋅ tan 1 7 ∘ = tan ( 4 5 ∘ − 1 7 ∘ ) = tan 2 8 ∘ = tan ( 9 0 ∘ − 6 2 ∘ ) = cot 6 2 ∘ \begin{aligned} & \text{ Let } \mathrm{I}=\frac{\cos 17^{{}^{\circ}}-\sin 17^{{}^{\circ}}}{\cos 17^{{}^{\circ}}+\sin 17^{{}^{\circ}}}=\frac{\cos 17^{{}^{\circ}}\left(1-\frac{\sin 17^{{}^{\circ}}}{\cos 17^{{}^{\circ}}}\right)}{\cos 17^{{}^{\circ}}\left(1+\frac{\sin 17^{{}^{\circ}}}{\cos 17^{{}^{\circ}}}\right)} \\ & \Rightarrow \mathrm{I}=\frac{\tan 45^{{}^{\circ}}-\tan 17^{{}^{\circ}}}{1+\tan 45^{{}^{\circ}} \cdot \tan 17^{{}^{\circ}}} \\ & =\tan \left(45^{{}^{\circ}}-17^{{}^{\circ}}\right)=\tan 28^{{}^{\circ}} \\ & =\tan \left(90^{{}^{\circ}}-62^{{}^{\circ}}\right)=\cot 62^{{}^{\circ}}\end{aligned} Let I = cos 1 7 ∘ + sin 1 7 ∘ cos 1 7 ∘ − sin 1 7 ∘ = cos 1 7 ∘ ( 1 + c o s 1 7 ∘ s i n 1 7 ∘ ) cos 1 7 ∘ ( 1 − c o s 1 7 ∘ s i n 1 7 ∘ ) ⇒ I = 1 + tan 4 5 ∘ ⋅ tan 1 7 ∘ tan 4 5 ∘ − tan 1 7 ∘ = tan ( 4 5 ∘ − 1 7 ∘ ) = tan 2 8 ∘ = tan ( 9 0 ∘ − 6 2 ∘ ) = cot 6 2 ∘
Practice Trigonometric Ratios & Identities on Quantrex Academy →
← Previous question What is the value of 65^ ^ ∘ +2 45^ ^ ∘ -2 40^ ^ ∘ - 25^ ^ ∘ ?Next question → What is 3 10^ ^ ∘ - 10^ ^ ∘ 25^ ^ ∘ 25^ ^ ∘ equal to?
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 2026 If α+ β=0= α+ β , α≠β then what is a value of 2α+ 2β+2 (α+β) ? NDA 2026 If 2 4β= 2α+ 2α , then which one of the following is a possible value of (α+β) ? NDA 2026 If x= θ- θ and y= θ+ θ , then which one of the following is correct ? NDA 2026 If θ=(1)/(3) , then what is the value of ((θ)/(2)) ((3θ)/(2)) ? NDA 2026 If A and B are acute angles such that 2A+2B=π , then what is the maximum value of A· B ? NDA 2026 x+ 3 x is maximum when x is equal to NDA 2026 In a triangle ABC , A= B+ C then what is ((B)/(2))+ ((B)/(2))equal to ? NDA 2026 If α and β are complementary angles such that α-β=(π)/(6) and m β=n α , then what is… NDA 2026 For the following two (02) items: Let A + B = p and A + B = q . What is (p^2 - q^2)/(p^2… NDA 2025 For the following two (02) items: Let p = cosec\, 20° and q = cosec\, 70° . What is (p^2… NDA 2025 For the following two (02) items: Let A + B = p and A + B = q . What is (p)/(q) equal to? NDA 2025 For the following two (02) items: Let p = cosec\, 20° and q = cosec\, 70° . What is ( 3… NDA 2025 Consider the following for the three (03) items that follow: Let p = 35° , q = 25° and r… NDA 2025 Consider the following for the three (03) items that follow: Let p = 35° , q = 25° and r… NDA 2025 Consider 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 PYQs JEE Mathematics PYQs
All NDA PYQs
