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viktelen [127]
2 years ago
14

prove that sin theta cos theta = cot theta is not a trigonometric identity by producing a counterexample

Mathematics
1 answer:
Zolol [24]2 years ago
5 0

Answer:

To prove that ( sin θ cos θ = cot θ ) is not a trigonometric identity.

Begin with the right hand side:

R.H.S = cot θ = \frac{cos \ \theta}{sin \ \theta}

L.H.S = sin θ cos θ

so, sin θ cos θ ≠ \frac{cos \ \theta}{sin \ \theta}

So, the equation is not a trigonometric identity.

=========================================================

<u>Anther solution:</u>

To prove that ( sin θ cos θ = cot θ ) is not a trigonometric identity.

Assume θ with a value and substitute with it.

Let θ = 45°

So, L.H.S = sin θ cos θ = sin 45° cos 45° = (1/√2) * (1/√2) = 1/2

R.H.S = cot θ = cot 45 = 1

So, L.H.S ≠ R.H.S

So, sin θ cos θ = cot θ is not a trigonometric identity.

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Answer:

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Since,

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-Which expression represents the phrase "twenty-three less than a number"? (Think about this one!)
4vir4ik [10]
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4 0
3 years ago
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Example 6
lapo4ka [179]

Answer:

The answer is below

Step-by-step explanation:

1. COST Mr. Rivera wants to purchase a riding lawn mower, which is on sale for 15% off the marked price.  The store charges sales tax 6.5% on all sales. Write a  function p(x) that represents the price after a 15%  discount. Write a function t(x) that represents the total  cost with sales tax. Write a composition of functions that  represents the total cost of a riding lawn mower on sale.  How much will Mr. Rivera pay for a riding lawn mower  that has a marked price of $3000?

Solution:

a) Let x represent the marked price and p(x) represent the price after discount. Since a discount of 15% is given, the price would be:

p(x) = x(100\% -15\%)=x(1-\frac{0.15}{100} )=0.85x

b) If x = discounted price and t(x) = total  cost with sales tax, then:

t(x) = x(100\% +6.5\%)=x(1+\frac{6.5}{100} )=1.065 x

c) Let t(x) represents the total  cost with sales tax

t[p(x)] =p(x)+6.5\%\ of\ p(x) \\\\t[p(x)] = 0.85x+(0.065*0.85x)\\\\t[p(x)] =0.90525x\\\\for\ x=\$3000:\\\\t[p(3000)] = 0.90525*3000=\$2715.75

8 0
3 years ago
What number is greatest?<br><br> 2 2/3,2.67,2 3/5,2.49
Anettt [7]
As a decimal, 2 2/3 is 2.67
2 3/5 is 2.6

So, the greatest is 2 2/3 and 2.67 because they are equivalent 
6 0
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