Test Index

ICSE Class X Math 2013 Paper

© examsnet.com
Question : 25 of 46
Marks: +1, -0
Show that 1−cos⁡A1+cos⁡A=sin⁡A1+cos⁡A\sqrt{\frac{1-\cos A}{1+\cos A}} = \frac{\sin A}{1+\cos A}
Solution:  
 L.H.S. =1−cos⁡A1+cos⁡A\text{ L.H.S. } = \sqrt{\frac{1-\cos A}{1+\cos A}}
Multiplying by 1+cos⁡A\sqrt{1+\cos A} in numerator and denominator
  =1−cos⁡A1+cos⁡A×1+cos⁡A1+cos⁡A\; = \sqrt{\frac{1-\cos A}{1+\cos A}} \times \sqrt{\frac{1+\cos A}{1+\cos A}}
  =(1−cos⁡A)(1+cos⁡A)(1+cos⁡A)(1+cos⁡A)\; = \sqrt{\frac{(1-\cos A)(1+\cos A)}{(1+\cos A)(1+\cos A)}}
  =1−cos⁡2A(1+cos⁡A)2=sin⁡2A(1+cos⁡A)2\; = \sqrt{\frac{1-\cos^2 A}{(1+\cos A)^2}} = \sqrt{\frac{\sin^2 A}{(1+\cos A)^2}}
  =sin⁡A1+cos⁡A= R.H.S. \; = \frac{\sin A}{1+\cos A} = \text{ R.H.S. }
© examsnet.com
Go to Question:
Prev Question
Next Question