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Find a if, a 27^{0}= ( 5+{5} )^{1/2}- ( 3-{5} )^{1/2}

Question

Find $a$ if, $a sin 2 7^{0} = (5 + 5)^{1/2} - (3 - 5)^{1/2}$

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Find

a

if,

a sin 2 7^{0} = (5 + 5)^{1/2} - (3 - 5)^{1/2}

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Text solutionVerified

Consier,

16 sin^{2} 2 7^{0}

= 8 (1 - cos 5 4^{0})

= 8 (1 - \frac{10 - 2 5}{4})

= 2 (4 - 10 - 25)

= 8 - 210 - 25

= (5 + 5) + (3 - 5) - 2 (5 + 5) (3 - 5)

= {5 + 5 - 3 - 5}^{2}

\Rightarrow

4 sin 2 7^{0} = 5 + 5 - 3 - 5

Ans: 4

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