Download App

Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
$\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{6}$ is equal to
  • ✓
    $\cot \left(7 \frac{1}{2}\right)^{\circ}$
  • B
    $\sin \left(7 \frac{1}{2}\right)^{\circ}$
  • C
    $\sin 15^{\circ}$
  • D
    $\cos 15^{\circ}$
✓

Answer

Correct option: A.
$\cot \left(7 \frac{1}{2}\right)^{\circ}$
(A)
$\cot \frac{A}{2}=\frac{1+\cos A}{\sin A}$
Putting $A =\left(7 \frac{1}{2}\right)^{\circ}$, we get
$\frac{1+\cos \theta}{\sin \theta}=\cot \frac{\theta}{2}$, where $\theta \neq 2 n \pi$
$\cot \left(7 \frac{1}{2}\right)^{\circ}=\frac{1+\cos 15^{\circ}}{\sin 15^{\circ}}=\frac{1+\frac{\sqrt{3}+1}{2 \sqrt{2}}}{\frac{\sqrt{3}-1}{2 \sqrt{2}}}$
$=\frac{2 \sqrt{2}+\sqrt{3}+1}{\sqrt{3}-1} \times \frac{\sqrt{3}+1}{\sqrt{3}+1}$
$=\sqrt{6}-\sqrt{3}+\sqrt{2}-2$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Trigonometry – II→Trigonometry – II — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $\tan \theta-\cot \theta=a$ and $\sin \theta+\cos \theta=b$, then $\left(b^2-1\right)^2\left(a^2+4\right)$ is equal to
→
If $\sin(\pi\cos\text{x})=\cos(\pi\sin\text{x}),$ then $\sin2\text{x}=$
→
$\lim _{x \rightarrow 0} \frac{\sin ^3 3 x}{x^3}=$
→
If $\left(\frac{3}{2}, \frac{5}{2}\right)$ is the midpoint of line segment intercepted by a line between axes, the equation of the line is
→
$1+\cos 2 x+\cos 4 x+\cos 6 x=$
→
Which of the following is incorrect?
→
$\lim _{x \rightarrow a} \frac{x^{-5}-a^{-5}}{x^{-3}-a^{-3}}=$
→
Mapping f : R $\rightarrow$ R which is defined as f(x) = cos x, x $\in$ R will be
→
If $1+\frac{1+2}{2}+\frac{1+2+3}{3}+\ ....$ to n terms is $S,$ then $S$ is equal to:
→
The number of diagonals that can be drawn by joining the vertices of an octagon is :
→