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1 − Sin θ Cos θ is Equal to - Mathematics

MCQ

\[\frac{1 - \sin \theta}{\cos \theta}\] is equal to

Options

  •  0

  • 1

  • sin θ + cos θ

  • sin θ − cos θ

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Solution

The given expression is ` sin θ/(1-cot θ)+ cos θ/(1-tan θ)` 

Simplifying the given expression, we have 

`sin θ/(1-cot θ)+ cos θ/(1-tan θ)` 

= `sinθ/(1-cosθ/sinθ)+cos θ/(1-sinθ/cos θ)`

=` sin θ/((sinθ-cos θ)/sin θ)+cos θ/((cos θ-sin θ)/cos θ)` 

= `sin^2θ/(sin θ-cos θ)+cos^2θ/(cos θ-sin θ)` 

= `sin^2θ/(sin θ-cos θ)+cos ^2θ/(-1(sin θ-cos θ))` 

= `sin ^2θ/(sin θ-cos θ)-cos ^2 θ/(sin θ-cos θ)` 

= `(sin^2θ-cos^2θ)/(sin θ-cos θ)` 

=` ((sinθ+cos θ)(sinθ-cos θ))/(sin θ-cos θ)`

=` sin θ+cos θ`

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 11 Trigonometric Identities
Q 8 | Page 57
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