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 cos: : Theta +sin: : Theta =sqrt {2}: : cos: : : Theta ,: : Find: : the;value ;of : : cos: : Theta -sin: : Theta

Right Option : C
View Explanation
Explanation
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
View Explanation
Explanation
Question : 3

If  large sin: : Theta +sin^2Theta =1,then : : cos^2Theta +cos^4Theta =

Right Option : C
View Explanation
Explanation
 
 
 


Students / Parents Reviews [20]