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adelina 88 [10]
3 years ago
15

Find an expression equivalent to 1-sinx ^2/1-cosx ^2

Mathematics
1 answer:
madam [21]3 years ago
8 0

Answer:

cot²x

Step-by-step explanation:

Using the identity

sin²x + cos²x = 1, then

1 - sin²x = cos²x

1 - cos²x = sin²x

Thus

\frac{1-sin^2x}{1-cos^2x} = \frac{cos^2x}{sin^2x} = cot²x

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satela [25.4K]

<u>Given </u><u>:</u><u>-</u>

  • A dealer sold a photocopy machine at Rs 4200 with 13% VAT to a retailer.
  • The retailer added transportation cost of Rs 250 , profit Rs 300 and local tax Rs 150 and sold to consumer .
  • Customer has to pay 13% VAT .

<u>To </u><u>Find </u><u>:</u><u>-</u>

  • Amount to be paid by the customer .

<u>Sol</u><u>u</u><u>tion </u><u>:</u><u>-</u>

Here , according to the question ,

\sf\dashrightarrow Cost\ of \ machine \ = \ Rs 4200

\sf\dashrightarrow VAT = 13\%

Therefore cost after adding VAT ,

\sf\dashrightarrow Cost = Cost_{initial}+13\% of Cost_{initial}\\

\sf\dashrightarrow Cost = Rs4200 + Rs 4200 \times \dfrac{13}{100}\\

\sf\dashrightarrow Cost = Rs4200 + Rs546\\

\sf\dashrightarrow \bf{ Cost = Rs 4746}

Again the values added by the retailer before selling to customer ,

  • Transport = Rs 250
  • Profit = Rs 300
  • Tax = Rs 150

Therefore total cost after adding these ,

\sf\dashrightarrow Cost = Rs( 4746+ 250+ 300 + 150 )\\

\sf\dashrightarrow\bf { Cost = Rs 5446}

Again Selling price after addition of 13% VAT ,

\sf\dashrightarrow SP = Rs 5446 + 13\% \ of \ Rs 5446\\

\sf\dashrightarrow SP = Rs 5446 + \dfrac{13}{100}\times 5446 \\

\sf\dashrightarrow SP = Rs (5446 + 707.98) =  Rs ( 5446 + 708)\\

\sf\dashrightarrow \underline{\underline{\bf SP_{to\ the \ customer} = Rs 6154}}

<u>Hence </u><u>the </u><u>amount </u><u>to </u><u>be </u><u>paid </u><u>by </u><u>the </u><u>customer </u><u>is </u><u>Rs </u><u>6</u><u>1</u><u>5</u><u>4</u><u> </u><u>.</u>

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