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

(1+tanTheta +secTheta )(1+cotTheta -cosecTheta )=

Right Option : C
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Explanation
Question : 2

If  cos: : Theta -sin: : Theta =sqrt {2}: : sin: : Theta , then  cos : : Theta +sin: : Theta =

Right Option : B
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Explanation
Question : 3

Simplify:  secTheta;.; cotTheta =

Right Option : C
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Explanation
 
 
 


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