8 feet less than the height . Make a algebraic expressions

Prove the following relations. Cos²A + cos²A.cot²A=cot²A (1-sin²A)(1+cot²A)=cot²A

mel-nik [20]

Step-by-step explanation:

Let's solve for the first one,

$R.H.S. = Cos²A + cos²A.cot²A$

Step 1- Take Cos²A common,

$= Cos²A( 1+ cot²A)$

$\small \sf \: Now \: we \: know \: that \\ \small (1 + Cot^{2} \theta = Cosec^{2} \theta)$

Step 2 - Substituting above value in step 1,

$= Cos^{2} A(Cosec^2A)$

$\small \sf \: We \: know \: that \: Cosec \theta= \frac{1}{Sin \theta}$

Step 3 - Substitute Cosec²A with 1/Sin²A

$= \frac{Cos^2A}{Sin^2A}$

$\small \sf \: Now \: the \: basic \: trigonometric \: function \: is \\ \small \frac{Cos\theta}{Sin \theta} = Cot\theta$

Step 4 - Replacing the product of step 3 with above function,

$= {Cot}^{2} A$

Hence proved,

$R.H.S = L.H.S$

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Now let's prove the second relation,

$(1-sin²A)(1+cot²A)=cot²A$

Let's solve for R.H.S.,

$R.H.S.= (1-sin^{2} A)(1+cot^{2} A)$

As I told above,

$\small(1+cot^{2} \theta) = cosec^{2} \theta$

Another important relation is,

$\small sin^2\theta + cos^2\theta= 1 \: or \: \\ \small cos^2\theta = 1 - sin^2\theta$

Replacing both the above brackets with this relation we get,

$= Cos^2A \cdot Cosec^2A$

Now follow the step 3 and step 4 of first question and you will get,

$R.H.S. = L.H.S.$

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Some important trigonometric relations that you must learn,

$Sin^2\theta + Cos^2\theta = 1 \\ 1 + Cot^2\theta = Cosec^2\theta \\ 1+Tan^2\theta = Sec^2\theta$

$\small\sf \: Thanks \: for \: joining \: brainly \: community!$

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These box plots show the basketball scores for two teams.

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Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

Kari and two of her friends are entering their senior year of high school. The tables below show the estimated expenses at three

vekshin1

The expenses for the duration of the four years that Kari will use in the university is $68600.

<h3>How to calculate expenses?</h3>

From the complete information, the expenses for the four years stay in the university will be calculated thus:

Tution = $8500

Room = $6700

Books = $1250

Miscellaneous expense = $700

Total = $17150

The expenses for the four years will be:

= $17150 × 4

= $68600

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a tool rental store charges a flat fee of $9.50 to rent a chain saw and $3.75 for each day including the first write an equation

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Answer:

y= 3.75x + 9.50

Step-by-step explanation:

3.75 per day

9.5 is the starting point

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2 years ago

In a certain instant lottery game, the chance of a win are stated as 7 in 22. Express the indicated degree of likelihood as a pr

katen-ka-za [31]

The probability value indication the degree of likelihood of 7 in 22 is 0.318

Given a degree of likelihood is 7 in 22 ; this can be interpreted thus :

Out of every 22 total outcomes or trials, the chance or possibility of winning is 7 times.

This can be expressed in probability terms as :

Probability = Required outcome / Total possible outcomes =

Probability = 7/22 = 0.31818

Therefore, the probability value for the degree of likelihood is 0.318

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3 years ago