The correct option is C 0 sin85^∘ sin35^∘ cos65^∘ =2 ( cos ( 85+352 )sin ( 85 352 ) ) cos 65 2cos60^∘sin25^∘ cos65^∘ =2 ( 12sin25^∘ ) ...

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Sin(A+B)Sin(A-B)

sin85∘-sin35∘...

Question

$sin 85^{\circ} - sin 35^{\circ} - cos 65^{\circ}$ =

0

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Solution

The correct option is C $0$
$sin 85^{\circ} - sin 35^{\circ} - cos 65^{\circ}$
$= 2 (cos (\frac{85 + 35}{2}) sin (\frac{85 - 35}{2})) - cos 65$
$2 cos 60^{\circ} sin 25^{\circ} - cos 65^{\circ}$
$= 2 (\frac{1}{2} sin 25^{\circ}) - cos 65^{\circ}$
$= sin 25^{\circ} - cos (90 - 25)$
$= sin 25^{\circ} - sin 25^{\circ}$
$= 0$

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sin 25^{\circ} . sin 35^{\circ} . sin 85^{\circ} = \frac{{cos x}^{\circ}}{a}

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(sin 35^{0} cos 55^{0} + cos 35^{0} sin 55^{0}) + \sqrt{3} (tan 10^{0} tan 30^{0} tan 80^{0}) = 2

{(\frac{s i n 35^{\circ}}{c o s 55^{\circ}})}^{2} + {(\frac{c o s 55^{\circ}}{s i n 35^{\circ}})}^{2} - 2 c o s 60^{\circ}

s i n 35^{\circ} s i n 55^{\circ} - c o s 35^{\circ} c o s 55^{\circ} = 0

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