Question

If
b
is any positive integer and
a
=
7
, applying Euclid’s division lemma
(
b
=
a
q
+
r
)
, the value of
r
can be:​

​

Answer 1

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

Answer 2

Euclid's division Lemma states that for any two positive integers 'a' and 'b' there exist two unique whole numbers 'q' and 'r' such that , a = bq + r, where 0≤ r < b. Here, a= Dividend, b= Divisor, q= quotient and r = Remainder. Hence, the values 'r' can take 0≤ r < b. Thus the value of r is 7.