Simplifying Trigonometric Expressions


 
 
Concept Explanation
 

Simplifying Trigonometric Expressions

To simplifying trigonometric expressions we should the relationship of the trigonometric ratios in terms of sine and cosine ratios. The steps to be followed are

1. Convert the various trigonometric ratios in terms of sine and cosine ratios.

2. Simplify the brackets using the rules of the BODMAS

3. Rationalise the remainder if required.  

Representing Trigonometric ratios in terms of sine and cosine ratio

tan;theta=frac{sin;theta}{cos;theta}

sec;theta=frac{1}{cos;theta}

cosec;theta=frac{1}{sin;theta}

cot;theta=frac{cos;theta}{sin;theta}

Illustration: Simplify the expression:

frac{tan; A}{ sin;A} + 1-frac{1}{cos; A}

Solution: To simplify this expression we will convert tan A in terms of sin A and cos A

frac{tan; A}{ sin;A} + 1-frac{1}{cos; A}

=frac{frac{sin ;A }{cos;A}}{frac{sin;A}{1}} + 1-frac{1}{cos; A}

=frac{sin ;A }{cos;A}times{frac{1}{sin;A}} + 1-frac{1}{cos; A}

 =frac{1}{cos;A} + 1-frac{1}{cos; A}

= 1

.... (More Text Available, Login?)
Sample Questions
(More Questions for each concept available in Login)
Question : 1

Simplify   tanA(cosA) + (1--sinA)

Right Option : C
View Explanation
Explanation
Question : 2

Simplify

sin Aleft (cos; A+ 2cosec;A right )- left ( frac{tan; A}{sec^2 A} right )

Right Option : C
View Explanation
Explanation
Question : 3

Simplify

sin^2 Aleft ( frac{cos A}{cot A} right )+ cos^2Aleft ( frac{sin A}{tan A} right )

Right Option : A
View Explanation
Explanation
 
 
 
Related Videos
Language - English



Students / Parents Reviews [20]