Question

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1.Evaluate

$\huge \frac{ \sin18 \degree}{ \cos72 \degree}$
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Answer 1

Solution :-

Before starting with the solution of this question, let us understand the concept.

Concept used:

cos also known as 'cosine' is the complimentary of sine as the name suggests.

So,

cos θ = sin (90 - θ)

Step-by-step explanation:

Applying this concept,

cos 72° can be written as sin (90° - 72°)

→ cos 72° = sin (90° - 72°)

⇒ cos 72° = sin 18°

Now, dividing by cos 72° on both sides,

$\sf{ \dfrac{cos \: 72^{ \circ} }{cos \: 72 ^{ \circ} } = \dfrac{sin \: {18}^{ \circ} }{ cos \: 72 ^{ \circ} } }$

$\implies \: \sf{ \dfrac{ \cancel{cos \: 72^{ \circ}} } { \cancel{cos \: 72 ^{ \circ}} } = \dfrac{sin \: {18}^{ \circ} }{ cos \: 72 ^{ \circ} } }$

$\implies \sf{ 1= \dfrac{sin \: {18}^{ \circ} }{ cos \: 72 ^{ \circ} } }$

$\therefore \: \boxed{ \bf{\dfrac{sin \: {18}^{ \circ} }{ cos \: 72 ^{ \circ} }} = 1}$