व सख्या मराक्त की नाही 2.5 कीजर 500
Answers
Answer:
Before starting with the solution of this question, let us understand the concept.
\begin{gathered}\\\end{gathered}
Concept used:
cos also known as 'cosine' is the complimentary of sine as the name suggests.
So,
cos θ = sin (90 - θ)
\begin{gathered}\\\end{gathered}
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°
\begin{gathered}\\\end{gathered}
Now, dividing by cos 72° on both sides,
\begin{gathered} \sf{ \dfrac{cos \: 72^{ \circ} }{cos \: 72 ^{ \circ} } = \dfrac{sin \: {18}^{ \circ} }{ cos \: 72 ^{ \circ} } } \\ \\ \end{gathered}
cos72
∘
cos72
∘
=
cos72
∘
sin18
∘
\begin{gathered} \implies \: \sf{ \dfrac{ \cancel{cos \: 72^{ \circ}} } { \cancel{cos \: 72 ^{ \circ}} } = \dfrac{sin \: {18}^{ \circ} }{ cos \: 72 ^{ \circ} } } \\ \\ \end{gathered}
⟹
cos72
∘
cos72
∘
=
cos72
∘
sin18
∘
\begin{gathered} \implies \sf{ 1= \dfrac{sin \: {18}^{ \circ} }{ cos \: 72 ^{ \circ} } } \\ \\ \end{gathered}
⟹1=
cos72
∘
sin18
∘
\begin{gathered} \therefore \: \boxed{ \bf{\dfrac{sin \: {18}^{ \circ} }{ cos \: 72 ^{ \circ} }} = 1} \\ \\ \end{gathered}
∴
cos72
∘
sin18
∘
=1