Question

Prove that
cot A - cos A
cosec A-1
cot A + cos A cosec A + 1​

Answer 1

Step-by-step explanation:

$\bold{\large{{\color{green}{ANSWER}}}}$

Answer:

\frac{cotA - cosA}{cotA+cosA}=\frac{cosecA-1}{cosecA+1}

cotA+cosA

cotA−cosA

=

cosecA+1

cosecA−1

Step-by-step explanation:

LHS =\frac{cotA - cosA}{cotA+cosA}LHS=

cotA+cosA

cotA−cosA

=\frac{\frac{cosA}{sinA}-cosA}{\frac{cosA}{sinA}+cosA}=

sinA

cosA

+cosA

sinA

cosA

−cosA

\begin{gathered}We\:know \:that \\\boxed {cotA= \frac{cosA}{sinA}}\end{gathered}

Weknowthat

cotA=

sinA

cosA

=\frac{cosA\left(\frac{1}{sinA}-1\right)}{cosA\left(\frac{1}{sinA}+1\right)}=

cosA(

sinA

1

+1)

cosA(

sinA

1

−1)

=\frac{\left(\frac{1}{sinA}-1\right)}{\left(\frac{1}{sinA}+1\right)}=

(

sinA

1

+1)

(

sinA

1

−1)

\begin{gathered}= \frac{cosecA-1}{cosecA+1}\\=RHS\end{gathered}

=

cosecA+1

cosecA−1

=RHS

Therefore,

\frac{cotA - cosA}{cotA+cosA}=\frac{cosecA-1}{cosecA+1}

cotA+cosA

cotA−cosA

=

cosecA+1

cosecA−1

•••♪

Answer 2

Answer:

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