Question

cos titha=60/100 then sin ×csc×tan×cot×sec=
​

Answer 1

Answer:

$\displaystyle{\boxed{\red{\sf\:\sin\:\theta\:\times\:\csc\:\theta\:\times\:\tan\:\theta\:\times\:\cot\:\theta\:\times\:\sec\:\theta\:=\:\dfrac{5}{3}}}}$

Step-by-step-explanation:

We have given that, $\displaystyle{\sf\:\cos\:\theta\:=\:\dfrac{60}{100}}$

We have to find the value of,

$\displaystyle{\sf\:\sin\:\theta\:\times\:\csc\:\theta\:\times\:\tan\:\theta\:\times\:\cot\:\theta\:\times\:\sec\:\theta}$

Now,

$\displaystyle{\sf\:\cos\:\theta\:=\:\cancel{\dfrac{60}{100}}}$

$\displaystyle{\implies\sf\:\cos\:\theta\:=\:\dfrac{3}{5}\:\:\:-\:-\:-\:(\:1\:)}$

Now,

$\displaystyle{\sf\:\sin\:\theta\:\times\:\csc\:\theta\:\times\:\tan\:\theta\:\times\:\cot\:\theta\:\times\:\sec\:\theta}$

$\displaystyle{\implies\sf\:\cancel{\sin\:\theta}\:\times\:\dfrac{1}{\cancel{\sin\:\theta}}\:\times\:\tan\:\theta\:\times\:\cot\:\theta\:\times\:\sec\:\theta\:\:\:-\:-\:-\:\left[\:\because\:\csc\:\theta\:=\:\dfrac{1}{\sin\:\theta}\:\right]}$

$\displaystyle{\implies\sf\:1\:\times\:\cancel{\tan\:\theta}\:\times\:\dfrac{1}{\cancel{\tan\:\theta}}\:\times\:\sec\:\theta\:\:\:-\:-\:-\:\left[\:\because\:\cot\:\theta\:=\:\dfrac{1}{\tan\:\theta}\:\right]}$

$\displaystyle{\implies\sf\:1\:\times\:\sec\:\theta}$

$\displaystyle{\implies\sf\:\sec\:\theta}$

$\displaystyle{\implies\sf\:\dfrac{1}{\cos\:\theta}\:\:\:-\:-\:-\:\left[\:\because\:\sec\:\theta\:=\:\dfrac{1}{\cos\:\theta}\:\right]}$

$\displaystyle{\implies\sf\:\dfrac{1}{\dfrac{3}{5}}\:\:\:-\:-\:-\:[\:From\:(\:1\:)\:]}$

$\displaystyle{\implies\sf\:1\:\times\:\dfrac{5}{3}}$

$\displaystyle{\implies\sf\:\dfrac{5}{3}}$

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:\sin\:\theta\:\times\:\csc\:\theta\:\times\:\tan\:\theta\:\times\:\cot\:\theta\:\times\:\sec\:\theta\:=\:\dfrac{5}{3}}}}}$

Answer 2

$\sf{\bold{\blue{\underline{\underline{Given}}}}}$

⠀⠀⠀⠀•$\bold{cos\theta=\dfrac{60}{100}   }$ 

$\sf{\bold{\red{\underline{\underline{To\:Find}}}}}$

$\bold{sin\theta ×cosec\theta ×tan\theta ×cot\theta ×sec\theta =??   }$ 

$\sf{\bold{\purple{\underline{\underline{Solution}}}}}$

HERE,

$\rightsquigarrow$ $\tt{cos\theta=\dfrac{60}{100}   }$ 

so,

$\hookrightarrow$ $\tt{cos\theta=\dfrac{\cancel{60}}{\cancel{100}}}$ 

$\hookrightarrow$ $\tt{cos\theta=\dfrac{6}{10}   }$ 

$\hookrightarrow$ $\tt{cos\theta=\dfrac{3}{5}   }$ 

Now,

$\implies{sin\theta ×cosec\theta ×tan\theta ×cot\theta ×sec\theta}$ 

$\rightsquigarrow$ $\tt{sin\theta× \dfrac{1}{sin\theta}× tan\theta× \dfrac{1}{tan\theta} ×sec\theta }$    

  

$\rightsquigarrow$ $\tt{\cancel{sin\theta}× \dfrac{1}{\cancel{sin\theta}}×\cancel{tan\theta}× \dfrac{1}{\cancel{tan\theta}} ×sec\theta  }$

$\rightsquigarrow$ $\tt{ 1×1×sec\theta  }$

$\rightsquigarrow$ $\tt{ sec\theta  }$

$\rightsquigarrow$ $\tt{\dfrac{1}{cos\theta}  }$

$\rightsquigarrow$ $\tt{\dfrac{1}{\dfrac{3}{5}}   }$

$\rightsquigarrow$ $\tt{\dfrac{1×5}{3}  }$

$\rightsquigarrow$ $\bold{\dfrac{5}{3}   }$ 

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

$\therefore$$\bold{sin\theta ×cosec\theta ×tan\theta ×cot\theta ×sec\theta =\dfrac{5}{3} }$ 

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