COMEDK · Maths · 8. Trigonometric Ratios & Identities
\(\text { Value of } \cos 105^{\circ} \text { is }\)
- A \(\dfrac{(\sqrt{3}+1)}{2 \sqrt{2}}\)
- B \(-\dfrac{(1-\sqrt{3})}{2 \sqrt{2}}\)
- C \(-\dfrac{(\sqrt{3}+1)}{2 \sqrt{2}}\)
- D \(-\dfrac{(\sqrt{3}-1)}{2 \sqrt{2}}\)
Answer & Solution
Correct Answer
(D) \(-\dfrac{(\sqrt{3}-1)}{2 \sqrt{2}}\)
Step-by-step Solution
Detailed explanation
The value of \(\cos 105^{\circ}\) can be calculated using the cosine addition formula \(\cos(A + B) = \cos A \cos B - \sin A \sin B\). We express \(105^{\circ}\) as \(60^{\circ} + 45^{\circ}\).…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If the foci of the ellipse \(\dfrac{x^2}{16}+\dfrac{y^2}{b^2}=1\) and the foci of the hyperbola \(\dfrac{x^2}{144}-\dfrac{y^2}{81}=\dfrac{1}{25}\) coincide, then the value of \(b^2\) isCOMEDK 2025 Medium
- If the matrix \(\left[\begin{array}{ccc}-3 & a-b & 5 \\ 1 & 0 & 4 \\ a+b & c & 11\end{array}\right]\) is symmetric then the value of \(a-b+c=\)COMEDK 2025 Medium
- The curve \(a x^3+b x^2+c x+d\) has a point of minima at \(x=1\), thenCOMEDK 2025 Medium
- The argument of the complex number \(\sin \left(\frac{6 \pi}{5}\right)+i\left(1+\cos \frac{6 \pi}{5}\right)\) isCOMEDK 2018 Medium
- The maximum value of \(Z=12 x+13 y\), subject to constraints \(x \geq 0, y \geq 0, x+y \leq 5\) and \(3 x+y \leq 9\) isCOMEDK 2023 Easy
- T. The angles \(A, B\) and \(C\) of a \(\triangle A B C\) are in A.P. If \(b: c=\sqrt{3}: \sqrt{2}\), then the angle \(A\) isCOMEDK 2019 Medium
More PYQs from COMEDK
- A six digit number is formed by using \(1,2,3,4\), 5,6 with no repetition. Then the probability that number 1 and 3 always come together.COMEDK 2024 Easy
- The equilibrium constant of given reaction is 100 .
\(\mathrm{N}_2(\mathrm{~g})+2 \mathrm{O}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_2\) (gas)
What is the equilibrium constant for the reaction given below?
\(\mathrm{NO}_2(g) \rightleftharpoons \frac{1}{2} \mathrm{~N}_2(g)+\mathrm{O}_2(g)\)COMEDK 2024 Hard - If for any \(2 \times 2\) square matrix \(A\),\(A(\operatorname{adj} A)=\left[\begin{array}{ll}8 & 0 \\ 0 & 8\end{array}\right]\), then find the value of \(\operatorname{det}(A)\).COMEDK 2022 Medium
- Fullerene with formula \(\mathrm{C}_{60}\) has a structure where every carbon atom isCOMEDK 2014 Easy
- A transition metal M forms 4 homoleptic octahedral coordination compounds, A, B, C and D of the type [MX6] \({ }^{z-}\) with monodentate ligands \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) and d respectively. These compounds absorb red, blue, yellow and blue-green light respectively. Which one of the options shows the correct order of decreasing ligand strength?COMEDK 2025 Medium
- If \(f(x)=\log _{x^{2}}(\log x)\), then \(f^{\prime}(x)\) at \(x=e\) isCOMEDK 2015 Easy