Question

Using which one of the following methods can you open the find &replica diolge

Answer 1

Answer:

† Question :-

Prove that ;

\begin{gathered} \boxed{ \boxed{ \rm \frac{sin \theta + tan\theta}{cos\theta} = tan\theta(1 + sec\theta) }} \bigstar\\ \end{gathered}

cosθ

sinθ+tanθ

=tanθ(1+secθ)

★

\large \dag† Step by step Solution :-

Taking Right Hand Side (RHS)

\begin{gathered} \: \: \: \: \rm tan\theta(1 + sec\theta) \\ \\ \end{gathered}

tanθ(1+secθ)

\begin{gathered} \small \rm = tan\theta \bigg(1 + \frac{1}{cos\theta} \bigg) \: \: \bigg\{\red{\because \sf sec\theta = \frac{1}{cos\theta} } \bigg\} \\\\ \end{gathered}

=tanθ(1+

cosθ

1

){∵secθ=

cosθ

1

}

\begin{gathered} \rm = tan\theta + \frac{tan\theta}{cos\theta} \\ \\ \end{gathered}

=tanθ+

cosθ

tanθ

\begin{gathered} \small \rm = \frac{sin\theta}{cos\theta} + \frac{tan\theta}{cos\theta} \: \: \bigg\{\red{\because \sf tan\theta = \frac{ sin\theta}{cos\theta} } \bigg\} \\\\ \end{gathered}

=

cosθ

sinθ

+

cosθ

tanθ

{∵tanθ=

cosθ

sinθ

}

⏩ Taking cosθ as LCM ;

\begin{gathered}\\ \large \pmb{ \purple{\rm = \frac{sin\theta + tan\theta}{cos\theta} } }\\ \\ \end{gathered}

=

cosθ

sinθ+tanθ

=

cosθ

sinθ+tanθ

which is your Left Hand Side (LHS)

\large \pink \maltese \: \: \underline{\orange{\underline{\frak{\pmb{\text Hence\:\:Proved }}}}}