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Use Trigonometric identities to simplify Trigonometric Expressions.

1. \(sin\theta +sin\theta cot^2 \theta \)

 

2. \((sin\theta -sin\theta cos^2 \theta )/sin^2 \theta \)

 

3. \((csc^2 \theta - cot^2 \theta )/cos\theta \)

 

4. \(sin\theta (csc\theta -sin\theta )\)

 

5.\(cosx+cosxtan^2 x\)

 

6.\(cos\theta csc\theta tan\theta \)

 Nov 29, 2019
 #1
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1.  sin θ   +  sin θ  cot^2 θ  =   sin θ (1 + cot^2 θ)  = sin θ * csc^2θ  =  sinθ (1/sin^2θ)  =

1/ sinθ  =  csc θ

 

2. (sin θ  -  sin θ  cos^2 θ)  / sin^2 θ  =    sin θ ( 1 - cos^2 θ) / sin^2 θ  =    sin θ ( sin^2θ) / sin^2θ  =

sin θ

 

3. (csc^2 θ - cot^2θ) / cos θ  =   1 / cos θ  =  sec θ

 

4. sin θ  ( csc θ  -  sin θ )  =  sin θ ( 1/sin θ  - sin θ)  =  1  - sin^2 θ  =  cos^2θ

 

5.  cos x + cos x  tan^2 x  =   cos x ( 1 + tan^2 x)  =   cos x  * sec^2 x  =   cos x *  1 / cos^2 x  =

1 / cos x   =  sec x

 

6. cosθ cscθ tan θ   =   cos θ  *  1 /sin θ  * sin θ  / cos θ  =   1

 

 

 

cool cool  cool

 Nov 29, 2019

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