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

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Sample Questions
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Question : 1

Simplify cot C . tan C

Right Option : C
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Question : 2

Simplify

cot; Aleft ( frac{1}{cosec A} right )+ sec;A- left ( frac{1}{sec; A} right )

Right Option : B
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Explanation
Question : 3

Simplify

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

Right Option : C
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