Find-cos 75-sin 15-sin 12-cos 78- - cos 18-sin 72-

Cos 75^∘/sin 15^∘+sin 12^∘/cos 78^∘ cos 18^∘/sin 72^∘ cos 75^∘/sin (90^∘ 75^∘)+sin 12^∘/cos (90^∘ 12^∘) cos 18^∘/sin (90^∘ 18^∘) =cos 75^∘/cos 75^∘+sin 12 ...

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Standard IX

Mathematics

Trigonometric Ratio(sin,cos,tan)

Find:cos 75∘/...

Question

Find:
$\frac{cos 75^{\circ}}{sin 15^{\circ}} + \frac{sin 12^{\circ}}{cos 78^{\circ}} - \frac{cos 18^{\circ}}{sin 72^{\circ}}$

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Solution

$\frac{cos 75^{\circ}}{sin 15^{\circ}} + \frac{sin 12^{\circ}}{cos 78^{\circ}} - \frac{cos 18^{\circ}}{sin 72^{\circ}}$

$\frac{cos 75^{\circ}}{sin (90^{\circ} - 75^{\circ})} + \frac{sin 12^{\circ}}{cos (90^{\circ} - 12^{\circ})} - \frac{cos 18^{\circ}}{sin (90^{\circ} - 18^{\circ})}$

$= \frac{cos 75^{\circ}}{cos 75^{\circ}} + \frac{sin 12^{\circ}}{sin 12^{\circ}} - \frac{cos 18^{\circ}}{cos 18^{\circ}} (∵ sin (90^{\circ} - θ) = cos θ a n d cos (90^{\circ} - θ) = sin θ)$

$= 1 + 1 - 1$

$= 1$

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Q. Find:

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$\frac{cos 75^{\circ}}{sin 15^{\circ}} + \frac{sin 12^{\circ}}{cos 78^{\circ}} - \frac{cos 18^{\circ}}{sin 72^{\circ}} =$ ______.

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Find: cos 75∘sin 15∘+sin 12∘cos 78∘−cos 18∘sin 72∘

cos 75∘sin 15∘+sin 12∘cos 78∘−cos 18∘sin 72∘ cos 75∘sin (90∘−75∘)+sin 12∘cos (90∘−12∘)−cos 18∘sin (90∘−18∘) =cos 75∘cos 75∘+sin 12∘sin 12∘−cos 18∘cos 18∘ (∵sin(90∘−θ)=cosθ and cos(90∘−θ)=sinθ) =1+1−1 =1

Find:
$\frac{cos 75^{\circ}}{sin 15^{\circ}} + \frac{sin 12^{\circ}}{cos 78^{\circ}} - \frac{cos 18^{\circ}}{sin 72^{\circ}}$