# If tan α = 1 − cos β sin β , then - Mathematics

MCQ

If $\tan \alpha = \frac{1 - \cos \beta}{\sin \beta}$ , then

#### Options

• $\tan 3 \alpha = \tan 2 \beta$

• $\tan 2 \alpha = \tan \beta$

• $\tan 2 \alpha = \tan \alpha$

• none of these

#### Solution

$\tan 2 \alpha = \tan \beta$
$tan\alpha = \frac{1 - cos\beta}{sin\beta}$
$= \frac{2 \sin^2 \frac{\beta}{2}}{2\sin\frac{\beta}{2}\cos\frac{\beta}{2}}$
$= \frac{\sin\frac{\beta}{2}}{\cos\frac{\beta}{2}}$
$\Rightarrow tan\alpha = \tan\frac{\beta}{2}$
$\Rightarrow \alpha = \frac{\beta}{2}$
$\Rightarrow 2\alpha = \beta$
$\therefore \tan2\alpha = tan\beta$

Concept: Values of Trigonometric Functions at Multiples and Submultiples of an Angle
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 9 Values of Trigonometric function at multiples and submultiples of an angle
Q 10 | Page 43