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