The value of 70^o + 470^o is - Vidyadip

MCQ

The value of $\cot {70^o} + 4\cos {70^o}$ is

A
$\frac{1}{{\sqrt 3 }}$
✓
$\sqrt 3 $
C
$2\sqrt 3 $
D
$\frac{1}{2}$

✓

Answer

Correct option: B.

$\sqrt 3 $

b
(b) Now, $\cot {70^o} + 4\cos {70^o} = \frac{{\cos {{70}^o} + 4\sin {{70}^o}\cos {{70}^o}}}{{\sin {{70}^o}}}$

$ = \frac{{\cos {{70}^o} + 2\sin {{140}^o}}}{{\sin {{70}^o}}} $

$= \frac{{\cos {{70}^o} + 2\sin ({{180}^o} - {{40}^o})}}{{\sin {{70}^o}}}$

$ = \frac{{\sin {{20}^o} + \sin {{40}^o} + \sin {{40}^o}}}{{\sin {{70}^o}}} $

$= \frac{{2\sin {{30}^o}\cos {{10}^o} + \sin {{40}^o}}}{{\sin {{70}^o}}}$

$ = \frac{{\sin {{80}^o} + \sin {{40}^o}}}{{\sin {{70}^o}}} $

$= \frac{{2\sin {{60}^o}\cos {{20}^o}}}{{\sin {{70}^o}}} = \sqrt 3 $.

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 3. trignometrical ratios,functions and identities→3. trignometrical ratios,functions and identities — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $f$ be an odd function defined on the set of real numbers such that for $x \geq 0$ , $f(x)\, =3\, sin\, x + 4\, cos\, x$. Then $f(x)$ at $x = - \frac{{11\pi }}{6}$ is equal to

Let $S$ be the set of all $(\alpha, \beta), \pi<\alpha, \beta<2 \pi$, for which the complex number $\frac{1-i \sin \alpha}{1+2 i \sin \alpha}$ is purely imaginary and $\frac{1+i \cos \beta}{1-2 i \cos \beta}$ is purely real. Let $Z_{\alpha \beta}=\sin 2 \alpha+i \cos 2 \beta,(\alpha, \beta) \in S$ . Then $\sum_{(\alpha, \beta) \in s }\left(i Z_{\alpha \beta}+\frac{1}{i \bar{Z}_{\alpha \beta}}\right)$ is equal to.

If $(a -2)x^2 + ay^2 = 4$ represents rectangular hyperbola, then $a$ equals :-

Let $P$ be an interior point of a $\triangle A B C$. Let $Q$ and $R$ be the reflections of $P$ in $A B$ and $A C$, respectively. If $Q, A, R$ are collinear, then $\angle A$ equals

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, is equal to

The fourth term in the expansion of $(x-2 y)^{12}$ is:

The value of $\sum_{r-1}^{18} cos^2(5r)^o,$ where $x^o $ denotes the $x$ degree, is equals to

If the lines ax + 12y + 1 = 0, bx + 13y + 1 = 0 and cx + 14y + 1 = 0 are concurrent, then a, b, c are in:

The length of the shortest path that begins at the point $(2,5),$ touches the $x-$ axis and then ends at a point on the circle

$x^2 + y^2 + 12x -20 y + 120 = 0$

If $\left( {{m_i},\frac{1}{{{m_i}}}} \right)\,\,,i = 1,2,3,4$ are con-cyclic points, then the value of ${m_1}.{m_2}.{m_3}.{m_4}$ is