Question

cos60°= 2 cos- 30° - 1​

Answer 1

Step-by-step explanation:

cos30= sqr(3)/2

cos60= 1/2

2cos^2(30) - 1 = cos60

2(cos30)^2 -1

2(sqr(3)/2)^2 -1

2(3/4) -1

3/2 -1

1/2

1/2 = cos60

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Answer 2

$\red{\large{\underline{\underline{ \rm{To \: Prove: }}}}}$

$\tt{ \cos60 \degree = 2 \cos - \: 30 \degree - 1}$

$\red{\large{\underline{\underline{ \rm{Let's \: Prove \: It: }}}}}$

L.H.S

We know value of cos 60°, So by putting the value we have:

$\tt{\cos60 \degree = \dfrac{1}{2}}$

R.H.S

$\tt2 \: { \cos}^{2} \: 30 \degree - 1$

➯ $\tt2 \: ({ \cos30 \degree) }^{2} - 1$

We know value of cos 30°, So by putting the value we have:

➯ $\tt2 \times （{ { \dfrac{ \sqrt{3} }{2}） }^{2} } - 1$

Now (√3)², √ and ² (sq) will get cancel and 2² = 4, So we have,

➯ $\tt（2 \times \dfrac{3}{4}） - 1$

➯ $\tt\dfrac{3}{2} - 1$

➯ $\tt{ \dfrac{3 - 2}{2} }$

➯ $\tt \dfrac{1}{2}$

L.H.S = R.H.S

$\green{ \underline{ \boxed{ \tt{ \dfrac{1}{2} = \dfrac{1}{2} }}}}$

$\sf{ \purple{Hence \: Proved!!}}$

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