1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sashaice [31]
3 years ago
12

Prove that :( 1 + 1/

smiddle" class="latex-formula">)(1 + 1/cot^{2}A) = 1/sin^{2}A - sin^{4}A
Mathematics
1 answer:
Aliun [14]3 years ago
3 0

Answer:

See explanation

Step-by-step explanation:

Simplify left and right parts separately.

<u>Left part:</u>

\left(1+\dfrac{1}{\tan^2A}\right)\left(1+\dfrac{1}{\cot ^2A}\right)\\ \\=\left(1+\dfrac{1}{\frac{\sin^2A}{\cos^2A}}\right)\left(1+\dfrac{1}{\frac{\cos^2A}{\sin^2A}}\right)\\ \\=\left(1+\dfrac{\cos^2A}{\sin^2A}\right)\left(1+\dfrac{\sin^2A}{\cos^2A}\right)\\ \\=\dfrac{\sin^2A+\cos^2A}{\sin^2A}\cdot \dfrac{\cos^2A+\sin^A}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A}\cdot \dfrac{1}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A\cos^2A}

<u>Right part:</u>

\dfrac{1}{\sin^2A-\sin^4A}\\ \\=\dfrac{1}{\sin^2A(1-\sin^2A)}\\ \\=\dfrac{1}{\sin^2A\cos^2A}

Since simplified left and right parts are the same, then the equality is true.

You might be interested in
Ten times the square of a non-zero number is equal to sixty times the number.
Mice21 [21]
Let x be the nonzero number.
10 x^{2} =60x \\  \frac{1}{10x}(10 x^{2} =60x) \\ x=6
7 0
3 years ago
Read 2 more answers
Given that lines m and n are parallel and that line t is a transversal, the
Naily [24]

Answer:

60

Step-by-step explanation:

if the opposite of <1 is 120 and the line it is sitting on is flat, we can figure out that both connected would be 180

the equation would be 180-120=60

hope this helped

3 0
2 years ago
Read 2 more answers
Solve -4(2x - 1) = -6(x + 2) - 2.<br><br> 1) -5<br><br> 2) 5<br><br> 3) 9<br><br> 4) -9
ad-work [718]

Answer:

The answer is x=9 so, its option 3.

4 0
2 years ago
Read 2 more answers
18y^8x^4w^6 and 30y^7w^3
djyliett [7]

Answer:

10

Step-by-step explanation:

6 0
3 years ago
Evaluate the expression for n=-3
satela [25.4K]

Answer:

5n is your answer hope this help

4 0
3 years ago
Other questions:
  • Write the ratio in three different formats:a to b, a:b, and a/b.
    15·1 answer
  • What algebraic expression shows the sum of 8 and x divided by 7
    10·1 answer
  • A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 290 people over
    10·1 answer
  • Find<br>a,b<br>such<br>that 7.2, a, b, 3 are in A.P.​
    7·1 answer
  • One serving of granola provides 4% of the protein you need daily. You must get the remaining 48 grams from other sources. How ma
    14·1 answer
  • Screenshot below
    8·2 answers
  • What is the decimal multiplier to increase by 58%?
    11·1 answer
  • Write a linear function f with the values f(-1)=-3 and f(2)=6.
    9·1 answer
  • Which expression is equivalent to 2(x + 7) - 2(9x - 0.4)?
    5·1 answer
  • Round-Trip Cost ($) Departure City Atlanta Salt Lake City Cincinnati 340.1 570.1 New York 321.6 354.6 Chicago 291.6 465.6 Denver
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!