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  • I have a doubt, kindly clarify. - Trigonometry - JEE Main-4

Find the value of \frac{1}{\cos72\degree} + \frac{1}{\sin54\degree}

  • Option 1)

    2

  • Option 2)

    \frac{1}{2}

  • Option 3)

    \frac{1}{2\sqrt5}

  • Option 4)

    2\sqrt5

 

Answers (1)

best_answer

As we have learnt,

 

Trigonometric Ratios of Important Angles -

\sin 18^{\circ}= \frac{\sqrt{5}-1}{4}

\cos 36^{\circ}= \frac{\sqrt{5}+1}{4}

- wherein

They can be derived if A= 18^{\circ}, 5A= 90^{\circ}

 

 \\*\Rightarrow \frac{1}{\sin18\degree} + \frac{1}{\cos36\degree} \\*\Rightarrow \frac{1}{\sqrt5 -\frac{1}{4}} + \frac{1}{\sqrt5 +\frac{1}{4}} \\*\Rightarrow 4\left(\frac{2\sqrt5}{5-1}\right) = 2\sqrt5

 


Option 1)

2

Option 2)

\frac{1}{2}

Option 3)

\frac{1}{2\sqrt5}

Option 4)

2\sqrt5

Posted by

Himanshu

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