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If Sin θ = `3/4` Show that `Sqrt((Cosec^2theta - Cot^2theta)/(Sec^2theta-1)) =Sqrt(7)/3` - Mathematics

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If sin θ = `3/4` show that `sqrt((cosec^2theta - cot^2theta)/(sec^2theta-1)) =sqrt(7)/3` 

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Solution

LHS = `sqrt((cosec^2theta - cot^2theta)/(sec^2 2-1))`

  =` sqrt(1/tan^2theta)`

=`sqrt(cot^2theta)`

= `cottheta`

= `sqrt(cosec^2theta -1)`

= `sqrt(1/(3/4)^2-1)`

=`sqrt((4/3)^2-1)`

=`sqrt(16/9-1)`

=`sqrt((16-9)/9)`

=`sqrt(7/9)`

=`sqrt(7)/3`

= RHS

Concept: Trigonometric Ratios and Its Reciprocal
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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 5 Trigonometric Ratios
Q 15
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