Skip Navigation Links
   
Trigonometric Ratio
To enroll in any of our courses, click here
 
   
Trigonometric Ratio: Trigonometric ratios of the angles are the ratios of the sides of a triangle with respect to its acute angles.

Trigonometric Identities: An equation involving trigonometric ratios of an angle (say) is said to be a trigonometric identity if it is satisfied for all values of for which the given trigonometric ratios are defined.

Here we will discuss how to use trigonometric identities in proving other trigonometric identities with help of some examples.

Example: Prove the following identities:

(i)cos4A - cos2A = sin4A - sin2A
(ii)sin4A + cos4A = 1 - 2 sin2A cos2 A

People who saw this lesson also found the following lessons useful:
AP : Sum of Finite Number
HCF and LCM
Conversion of Solids
Probability
Distance Between Two Points
Solution:
(i) Given:
LHS
= cos4A - cos2A
= cos2A (cos2A - 1)
= -cos2A (1 - cos2A)
= -cos2A sin2A
= -1(1 - sin2A) sin2A
= -sin2A + sin4A
= sin4A - sin2A = RHS

(ii) Given:
LHS
= sin4A+ cos4A
= (sin2A)2 (cos2A)2+ 2 sin2A cos2A - 2 sin2Acos2A
= (sin2A + cos2A)2 - 2 sin2A cos2A
= 1 - 2 sin2A cos2A = RHS
.
 
   
As many of you know, Winpossible's online courses use a unique teaching method where an instructor explains the concepts in any given area to you in his/her own voice and handwriting, just like you see your teacher explain things to you on a blackboard in your classroom. All our courses include teacher's instruction, practice questions as well as end-of-lesson quizzes for practice. You can enroll in any of our online courses by clicking here.

The format of Winpossible's online courses is also very suitable for teachers who are using an interactive whiteboard such as Smartboard on Promethean in their classrooms, because the course lessons can be easily displayed on such interactive whiteboards. Volume pricing is available for schools interested in our online courses. For more information, please contact us at educators@winpossible.com.

 
       
     
 Copyright © Winpossible, 2010 - 2011
Best viewed in 1024x768 & IE 5.0 or later version
l>