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(Cosec θ − Sin θ) (Sec θ − Cos θ) (Tan θ + Cot θ) is Equal to - Mathematics

MCQ

(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to

Options

  • 0

  • 1

  •  −1

  • None of these

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Solution

None of these 

`(cosec ecθ-sinθ)(secθ-cos θ)(tan θ+cot θ)` Simplifying the given expression, we have 

`(cosec θ-sinθ)(secθ-cosθ)(tanθ+cot θ)`

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

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

=` cos^2θ/sin θ xx sin^2θ/cosθxx1/(sinθ cosθ)` 

=`(cos^2θ sin^2θ)/(sin^2θ cos^2θ)`

= `1`

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APPEARS IN

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