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Some Applications Of Trigonometry

Question

If sin θ = 1/3, then find the value of (2 cot²θ+ 2).

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Solution

2cot² θ + 2 =2 (cosec²θ - 1) + 2
= 2 cosec² θ -2 + 2
= 2 cosec² θ

fraction numerator 2 over denominator sin squared straight theta end fraction space equals space fraction numerator 2 over denominator 1 divided by 9 end fraction space space equals space 18.