Advertisement Remove all ads

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 

Advertisement Remove all ads

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?
Advertisement Remove all ads

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
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×