Question

prove that:sin 60° . cos 30° + cos 60°.sin
30°=1​

Answer 1

$\huge\underline{\red{\boxed{\tt{To \:prove }}}}$

sin °60.cos 30° + cos 60°.sin 30° = 1

$\huge\underline{\boxed{\red{\tt{We\: know\: that}}}}$

• sin 60° = cos 30°

$\tt{\because sin 60\degree = \frac{\sqrt{3} }{2} = cos30\degree$

• cos 60° = sin 30°

$\tt{\becuase \: sin30\degree = cos60\degree = \frac{1}{2}$

$\huge\underline{\boxed{\green{\tt{Let's \: Prove}}}}$

$\tt{ \implies sin60\degree = cos30\degree}$

$\tt{\implies sin60\degree.cos30\degree = sin60\degree . sin60\degree$

$\tt{\implies \: sin60\degree . cos30\degree = sin^{2} 60\degree \:\:\:\:eq-1}$

$\tt{\implies\: cos60\degree = sin30\degree}$

$\tt{\implies \: cos60\degree.sin30\degree = cos60\degree . cos60\degree}$

$\tt{\implies\: cos60\degree.sin30\degree = cos^{2} 60\degree\:\:\:\:eq-2}$

$\tt{ so\: from\: eq-1 \: and \: eq-2 ,\: we\: get\: that}$

$\tt{\implies sin60\degree.cos30\degree + cos60\degree.sin30\degree}$

$\tt{\implies \: sin^{2}60\degree + cos^{2} 60\degree$

$\tt{as\: we\: know\: that\: , sin^{2} 60\degree +cos^{2} 60\degree = 1$

$\tt{\implies sin60\degree.cos30\degree + cos60\degree.sin30\degree = sin^{2} 60 \degree + cos^{2}60\degree = 1}$

hence, proved .

Additional information :

$\tt{\bull \: sin^{2}\theta + cos^{2}\theta = 1}$

$\tt{\bull\: sec^{2}\theta-tan^{2}\theta = 1}$

$\tt{\bull \: cosec^{2}\theta-cot^{2} \theta = 1}$

$\tt{sec60\degree= cos30\degree}\\\tt{cos60\degree = sin60\degree}\\\tt{sin0\degree = cos90\degree}\\\tt{cos45\degree = sin45\degree}$

Answer 2

Prove that:sin 60° . cos 30° + cos 60°.sin

30°=1​

1

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YourHelperAdi

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sin °60.cos 30° + cos 60°.sin 30° = 1

sin 60° = cos 30°

cos 60° = sin 30°

hence, proved .

Additional information :

arrenhasyd and 3 more users found this answer helpful

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may be the net is slow so the answer is not is visible