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InterviewSolution
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If cotθ = 3 then find the value of the expression \(\frac{{9{\rm{sin\theta \;}} + {\rm{\;}}7{\rm{cos\theta \;}}}}{{{\rm{co}}{{\rm{s}}^3}{\rm{\theta \;}} + {\rm{\;}}3{\rm{si}}{{\rm{n}}^3}{\rm{\theta \;}} + {\rm{\;}}5{\rm{sin\theta \;}}}}\)1). 15/42). 53). 30/74). 6 |
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Answer» $(\frac{{9{\rm{sin\theta \;}} + {\rm{\;}}7{\rm{cos\theta \;}}}}{{{\rm{CO}}{{\rm{s}}^3}{\rm{\theta \;}} + {\rm{\;}}3{\rm{si}}{{\rm{n}}^3}{\rm{\theta \;}} + {\rm{\;}}5{\rm{sin\theta \;}}}})$ DIVIDING the expression by sinθ $(\Rightarrow {\rm{\;}}\frac{{9{\rm{\;}} + {\rm{\;}}7{\rm{cot\theta \;}}}}{{{\rm{cot\theta \;co}}{{\rm{s}}^2}{\rm{\theta \;}} + {\rm{\;}}3{\rm{si}}{{\rm{n}}^2}{\rm{\theta \;}} + {\rm{\;}}5{\rm{\;}}}})$ $(\Rightarrow {\rm{\;}}\frac{{9{\rm{\;}} + {\rm{\;}}7{\rm{cot\theta \;}}}}{{{\rm{cot\theta \;co}}{{\rm{s}}^2}{\rm{\theta \;}} + {\rm{\;}}3{\rm{si}}{{\rm{n}}^2}{\rm{\theta \;}} + {\rm{\;}}5{\rm{\;}}}})$ Putting cotθ = 3 $(\Rightarrow {\rm{\;}}\frac{{30{\rm{\;}}}}{{3{\rm{co}}{{\rm{s}}^2}{\rm{\theta \;}} + {\rm{\;}}3{\rm{si}}{{\rm{n}}^2}{\rm{\theta \;}} + {\rm{\;}}5{\rm{\;}}}})$ $(\Rightarrow {\rm{\;}}\frac{{30{\rm{\;}}}}{{3({\rm{co}}{{\rm{s}}^2}{\rm{\theta \;}} + {\rm{\;si}}{{\rm{n}}^2}{\rm{\theta }}){\rm{\;}} + {\rm{\;}}5{\rm{\;}}}}{\rm{}} = {\rm{}}\frac{{15}}{4})$ $(\therefore {\rm{\;}}\frac{{9{\rm{sin\theta \;}} + {\rm{\;}}7{\rm{cos\theta \;}}}}{{{\rm{co}}{{\rm{s}}^3}{\rm{\theta \;}} + {\rm{\;}}3{\rm{si}}{{\rm{n}}^3}{\rm{\theta \;}} + {\rm{\;}}5{\rm{sin\theta \;}}}}{\rm{}} = {\rm{}}\frac{{15}}{4})$ |
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