Question

Verify the identity. (8 points)
cot^2 x/csc x + 1 = 1 - sinx/ sin x
i really need help

Answer 1

is it this

\(\large \begin{align} \color{black}{
\dfrac{\cot^2 x}{\csc x} + 1 = 1 - \dfrac{\sin x}{ \sin x} \hspace{.33em}\\~\\
or ~~this \hspace{.33em}\\~\\
\dfrac{\cot^2 x}{\csc x} + 1 = \dfrac{1-\sin x}{ \sin x} \hspace{.33em}\\~\\
}\end{align}\)

Answer 2

let me attach a photo

Answer 3

here it is

Answer 4

@mathmath333

Answer 5

\(\large \begin{align} \color{black}{
\dfrac{\cot^2x}{\csc x-1} \hspace{.33em}\\~\\
=\dfrac{\cot^2x}{\csc x-1}\times \dfrac{\csc x+1}{\csc x+1} \hspace{.33em}\\~\\
=\dfrac{\cot^2x\times (\csc x+1)}{\csc^2 x-1} \hspace{.33em}\\~\\
=\dfrac{\cot^2x\times (\csc x+1)}{\csc^2 x-1} \hspace{.33em}\\~\\
=\dfrac{\cot^2x\times (\csc x+1)}{\cot^2x} \hspace{.33em}\\~\\
=\csc x+1 \hspace{.33em}\\~\\
=\dfrac{1}{\sin x}+1 \hspace{.33em}\\~\\
}\end{align}\)

see if it makes sense

Answer 6

thats only part of it right?

Answer 7

csc x+1 denominator

Answer 8

can u show me step by step to get the answer and then what the answer would be

Answer 9

yes 99%

the last part can be written as


\(\large \begin{align} \color{black}{

=\dfrac{1}{\sin x}+1 \hspace{.33em}\\~\\
=\dfrac{1+\sin x}{\sin x} \hspace{.33em}\\~\\
}\end{align}\)

now see if it does match with th question given

Answer 10

well what I'm trying to understand is why you switched csc x + 1 to a negative 1

Answer 11

u mean this red part
\(\large \begin{align} \color{black}{
\dfrac{\cot^2x}{\csc x-1} \hspace{.33em}\\~\\
=\dfrac{\cot^2x}{\csc x-1}\times \color{red }{\dfrac{\csc x+1}{\csc x+1} }\hspace{.33em}\\~\\
=\dfrac{\cot^2x\times (\csc x+1)}{\csc^2 x-1} \hspace{.33em}\\~\\
=\dfrac{\cot^2x\times (\csc x+1)}{\csc^2 x-1} \hspace{.33em}\\~\\
=\dfrac{\cot^2x\times (\csc x+1)}{\cot^2x} \hspace{.33em}\\~\\
=\csc x+1 \hspace{.33em}\\~\\
=\dfrac{1}{\sin x}+1 \hspace{.33em}\\~\\
}\end{align}\)

Answer 12

yes and what happened to the right of the problem????

Answer 13

1 - sinx and sin x

Answer 14

no thing happened the question says verify the identity as the last part doesnt matches the one given in the question,
the given identity is \(\bf false\)

amd about the red part do u agree that
\(\large \dfrac{\csc x+1}{\csc x+1}=1\) ?

Answer 15

yes so what should i submit as an an answer and they want the work

Answer 16

if they want work , show as i did upto
\(\dfrac{1+\sin x}{\sin x}\) and write that

\(LHS\neq RHS\)

so its false

Answer 17

that red part i did was to rationalise the denominator

Answer 18

thank you for everything