Math, asked by neerajkhaden, 10 months ago

If cotA =√3 find the value of cosec2A +cot2A /cosec2A-sec2A

Answers

Answered by narissa050707
0

Answer: Discount = D% of marked price, M

Discount = Marked Price – Selling Price

Marked Price – Amount of Discount = Selling Price

M (1-D%) = Selling Price

Also, Selling Price = Cost Price + Gain

Thus,

M (1-D%) = C (1 + G%)

Or in other words

Marked Price (1 – Discount%) = Cost Price (1 + Gain%)

Example-1: Natasha offers her customers a discount of 10% on her beauty products and she still makes a profit of 20%. What is the actual cost to her of that beauty product marked Rs. 400?

Solution:

Marked price = Rs. 400

Discount = 10%

Profit = 20%

Therefore, the Selling Price = 90% of 400

Therefore 400 x 90/100 = Rs. 360

Selling price = Rs. 360

Profit = 20%

Cost price = 100/120 x 360 = Rs. 300

Profit and Loss: Concept of successive discounts

If successive discounts of x% and y% are allowed on the marked price M of the discount, then, after discount the customer finally ends up paying:

Selling Price = (1-x%)(1-y%) x Marked Price

If you look at the above formula closely, you would see that the multiplication is nothing else but a percentage equivalent of two successive percentage change on a number.

Example-2: Pankaj offers a 10% discounts on his goods and he offers a further discount of 5% on the reduced price to those customers who pay cash. What does a customer have to pay in cash for a cricket bat of Rs. 200?

Solution:

Price of the cricket bat = Rs. 200

After Discount of 10% Marked price would be Rs. 180

Since he is purchasing the bat by cash, so a discount of 5% is applicable again on the reduced marked price. Thus, the final selling price the cricket bat would be of Rs. 171

Profit and Loss: Basic Question types

Type-1: Comparing quantities of goods and prices

In these types of questions, CP of a fixed number of goods are compared with the SP of another field number of goods. Let us see through an example:

Example-3: The cost price of 30 articles is equal to the selling price of 40 articles. What is the profit or loss percentage?

Solution:

To obtain the same amount of money, which was needed to purchase 30 articles, we need to sell 40 articles, which is more than what we have got for the same sum. It means we need to arrange 10 more articles apart from the articles which we have purchased. So, there will be a loss.

Now, CP of 30 articles = SP of 40 articles Or, CP/SP = 30/40 =3/4

Or, 1 – CP/SP = 1- 3/4 = 1/4

So, Loss percentage

= (l – CP/SP) x 100 = 1/4x 100 = 25%

Alternatively,

CP of 30 articles = SP of 40 articles = Rs 120 (Assume) So, CP of one article = Rs 4 ,SP of one article = Rs 3 Obviously, there is a loss of Re 1 Loss percentage = 1,4 X 100 = 25%

Type 2: Questions in terms of money

In this type of question, we generally talk about the cost price and selling price questions there are some results which helps us to solve typical these type of questions

Some Important Results

When SPs of two articles are same

1. First one is sold at a profit of x% and second one is sold at a profit of y%.

Ratio of CP1:CP2 (100 + y) : (100 + x)

2. First one is sold at a profit of x% and second one is sold at a loss of y%.

Ratio of CP1:CP2 = (100 – y): (100 + x)

3. First one is sold at a loss of x% and second one is sold at a loss of y%.

Ratio of CP1: CP2 = (100 – y): (100 – x)

4. First one is sold at a loss of x% and second one is sold at a profit of y%.

Ratio of CP1: CP2 = (100 + y): (100 – x)

Type-3: Miscellaneous Problems based on % gain and % loss

Example-4: Bharat purchased 90 bags of cement at Rs. 450 each. He sold 30 bags at 20% profit and 20 bags at 6% loss. At what rate per bag should the remainder he sold to gain a profit of 9% on whole transaction

Solution:

This question type is nothing else but a combination of ratio and proportion with profit and loss. In this case, we can solve the question in the following manner:

According to the information given, bags remaining = 40

Let the 40 bags be sold with p% gain

Now % gain or loss on the whole lot

= sum of product of gain or loss %s with their respective quantities

Therefore

9% of 90 Bags of Rs. 450 each = 20% of 30 Bags of Rs. 450 each – 6% of 20 Bags of Rs. 450 each +9% of 40 Bags of Rs. 450 each

(9/100) x 90 x 450= {(20/100) x 30 x 450} – {(6/100) x 20 x 450} + {(p/100) x 40 x 450}

9 x 90 = (20 x 30) – (6 x 20) + (p x 40)

p = 8.25%

Therefore, the selling price would be = 108.25/100 x 450 = Rs. 487.125

Step-by-step explanation:

Answered by rani49035
1

Answer:

cotA =√3

thus A = 30°

put A= 30° in the above question..

we get

(cosec2(30) + cot2(30))/(cosec2(30) - sec2(30))

(cosec60° + cot60°)/(cosec60° -sec60°)

put their values..

we get (2/√3 + 1/√3)/(2/√3 - 2)

=( 3/√3) / (2 - 2/√3)/√3

= (√3)/(2-2√3)/√3

=3/ (2-2√3)

hope this will help you

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