Math, asked by ITZINNOVATIVEGIRL588, 10 months ago

what is the value of Cos 36° ?

In detail.......​

Answers

Answered by MH99
4

Answer:

If you calculate it aiding 991ES calculator then the answer comes to

0.809016...(approx)

Answered by Anonymous
54

To find:-

cos36° = ?

Solution:-

Let β = 18° .Then,

β = 18° => 5β = 90°

⠀⠀⠀ ⠀=> 3β+2β = 90°

⠀⠀⠀ ⠀=> 2β = 90° - 3β

⠀⠀ ⠀⠀=> sin2β = sin(90°-3β) = cos3β

⠀⠀⠀⠀ => 2sinβ cosβ = 4cos³β - 3cosβ

⠀ ⠀=> 2sinβcosβ - 4cos³β + 3cosβ = 0

⠀⠀⠀⠀ => cosβ(2sinβ - 4cos²β + 3) = 0

⠀⠀ ⠀⠀=> 2sinβ - 4cos²β + 3 = 0

⠀⠀⠀⠀ => 2sinβ - 4(1-sin²β) + 3 = 0

⠀⠀ ⠀=> 4sin²β + 2sinβ -1 = 0

According to Sri Dharacharya formula

⠀⠀⠀⠀

 =  > sin \beta  =  \frac{ - 2 ±  \sqrt{4 + 16} }{8}   \\  =  > sin \beta  =   \frac{ - 2 ± \sqrt{20} }{8}  =   \frac{ - 2 ± 2 \sqrt{5} }{8}   \\  =  > sin \beta  =   \frac{2( -1 ± \sqrt{5}) }{8}  =  >   \frac{ \sqrt{5} - 1 }{4}   \\  =  > sin \beta  =  \frac{ \sqrt{5} - 1 }{4}

As we are supposed that β= 18°

Then,

sin18 =  \frac{ (\sqrt{5} - 1) }{4}

Now for cos18°

=> cos36° = cos(2×18) = (1 - 2sin²18°)

=> cos36° =   1 - 2 \frac{ {( \sqrt{5 }  - 1)}^{2} }{16}  = 1 -  \frac{6 - 2 \sqrt{5} }{8}

 =  >cos36 =  \frac{ \sqrt{5}  + 1}{4}

Hence proved.

Hope its help uh

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