Choose the correct answer from the given four options. If 9 = and… - Vidyadip

MCQ

Choose the correct answer from the given four options.
If $\cos9\alpha=\sin\alpha\text{ and }9\alpha<90^\circ,$ then the value of $\tan5\alpha$ is:

A
$\frac{1}{\sqrt{3}}$
B
$\frac{\sqrt{3}}{1}$
✓
$1$
D
$0$

✓

Answer

Correct option: C.

$1$

$\sin(90^\circ-9\alpha)=\sin\alpha$ $[\because\cos\text{A}=\sin(90^\circ-\text{A})]$
$\Rightarrow\ \ 90^\circ-9\alpha=\alpha$
$\Rightarrow\ \ 10\alpha=90^\circ$
$\Rightarrow\ \ \alpha=9^\circ$
$\therefore\tan5\alpha=\tan(5\times9^\circ)=\tan45^\circ=1$
$[\because\tan45^\circ=1]$

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 "M.C.Q (1 Marks)" from Introduction of Trigonometry and its Application→Introduction of Trigonometry and its Application — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

A tangent $PQ$ at point of contact $P$ to a circle of radius $12\ cm$ meets the line through centre $O$ to a point $Q$ such that $OQ = 20\ cm,$ length of tangent $PQ$ is :

The difference of a rational and an irrational number is always :

If $\tan\theta=\frac{8}{15}$ then $\text{cosec}\theta=?$

The root of a quadratic equation are $5$ and $-2$. Then, the equation is :

The radius of the base of a cone is 5cm and its height is 12cm. Its curved surface area is:

The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is

The disrtance of point P(2, 3) from the X-axis is:

A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken together, is :

The distance of the point $(-3, 4)$ from the origin is :

$\sec ^4 A-\sec ^2 A$ is equal to