Prove the identity (cot x sin x)(sec x – cos x) = sin^2x

Mathematics

2 answers:

hram777 [196]3 years ago

8 0

Answer:

[(cosx/sinx)(sinx)][(1/cosx) - cosx]

(cosx)[(1 - cos²x)/cosx]

1 - cos²x

sin²x

FrozenT [24]3 years ago

7 0

Step-by-step explanation:

$(cot x \: sinx)(secx - cosx) = {sin}^{2} x \\ \\ lhs = (cot x \: sinx)(secx - cosx) \\ = (cot x \: sinx) \times secx \\- (cot x \: sinx) \times cosx \\ \\ = \frac{cosx}{sinx} \times sinx \times secx\\ - \frac{cosx}{sinx} \times sinx \times cosx \\ = cosx \times secx - cosx \times cosx \\ = 1 - {cos}^{2} x \\ = {sin}^{2} x \\ = rhs \\ hence \: proved$

You might be interested in

1st question: Reuben received 80 dollars. Write a signed number to represent this change.

lesya692 [45]

Answer:

1) +80

2) -1520

Step-by-step explanation:

Positive Signed numbers are used in real world situations to indicate the increase. Examples include; increase in weight, deposit of money into an account, increase in income, profit, height above sea level, etc. They are all represented by positive signed numbers.

Whereas, negative signed numbers show decrease. Examples include; loss of weight, withdrawal of money from an account, loans, liabilities, losses, temperature below zero degrees, height below sea level.

1) We are told that Reuben received 80 dollars. Thus, it means he received an increase in the amount of money he already had. Thus, the signed number will be +80.

2) We are told that A car corporation produced 1520 fewer cars this month than last.

Thus, the signed number will be negative since there is a decrease in number of cars.

Thus, signed number = -1520

7 0

3 years ago

34. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.

skad [1K]

Answer:

The linear equation for the line which passes through the points given as (-1,4) and (5,2), is written in the point-slope form as $y=\frac{1}{3} x-\frac{13}{3}$ .

Step-by-step explanation:

A condition is given that a line passes through the points whose coordinates are (-1,4) and (5,2).

It is asked to find the linear equation which satisfies the given condition.

Step 1 of 3

Determine the slope of the line.

The points through which the line passes are given as (-1,4) and (5,2). Next, the formula for the slope is given as,

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substitute 2&4 for $y_{2}$ and $y_{1}$ respectively, and $5 \&-1$ for $x_{2}$ and $x_{1}$ respectively in the above formula. Then simplify to get the slope as follows,