Trigonometric Identities


 
 
Concept Explanation
 

Trigonometric Identities

Trigonometric Identities: The trigonometric identities are equalities which are true for every value appearing on both sides of the equal sign An equation involving trigonometric ratios of an angle is called a trigonometric identity, if it is true for all values of the angle(s) involved. These identities are useful whenever expressions involving trigonometric ratios are to be simplified.

sin^2;theta + cos^2;theta = 1

sec^2;theta - tan^2;theta = 1

cosec^2;theta - cot^2;theta = 1

Illustration: Simplify the expression:

frac{sin Theta -2 sin^3Theta }{2 cos^3Theta -cos Theta }

Solution: We will simplify the expression using trigonometric Identities

frac{sin Theta -2 sin^3Theta }{2 cos ^3Theta -cos Theta }   =   frac{sin Theta (1-2 sin^2Theta )}{cos Theta (2 cos ^2Theta -1)}

                                  =tan;Theta left (frac{1-2(1-cos^2Theta )}{2 cos^2Theta -1} right)

                                 =tan;Theta left (frac{1-2 +2cos^2Theta )}{2 cos^2Theta -1} right)

                                 =tan Theta left (frac{2 cos^2Theta -1}{2 cos^2Theta -1} right)

                                 =tan Theta

=

                   

Sample Questions
(More Questions for each concept available in Login)
Question : 1

If  large Delta ABC  is right angled at C, then the value of cos (A + B) is

Right Option : A
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Question : 2

If b tan Theta =a, the value of frac{asinTheta b cos Theta }{a sin Theta +b cos Theta } is

Right Option : D
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Explanation
Question : 3

GIven that large sin : : alpha =frac {1}{2}and : : cos: beta =frac {1}{2}, then the value of large (alpha +beta ) is

Right Option : D
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Explanation
 
 
 


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