Question

without using trigonometric tables prove that cos 81 degree minus sin 9 degree equal to zero

Answer 1

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Answer 2

Without using trigonometric tables proved that cos 81 degree minus sin 9 degree equal to zero

Solution:

Given that,

We have to prove:

$cos\ 81^{\circ} - sin\ 9^{\circ} = 0$

Take LHS

$cos\ 81^{\circ} - sin\ 9^{\circ}$

We know that,

$cos(90 - \theta) = sin\ \theta$

Therefore,

$sin\ 9 = cos(90 - 9) = cos\ 81$

Thus, the given becomes:

$cos\ 81^{\circ} - sin\ 9^{\circ}\\\\cos\ 81^{\circ} - cos\ 81^{\circ} \\\\0$

Thus,

$cos\ 81^{\circ} - sin\ 9^{\circ} = 0$

Thus proved

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