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
Lunna [17]
2 years ago
5

Prove :sin²θ + cos²θ = 1thankyou ~​

Mathematics
1 answer:
Gnom [1K]2 years ago
5 0

Answer:

See below

Step-by-step explanation:

Here we need to prove that ,

\sf\longrightarrow sin^2\theta + cos^2\theta = 1

Imagine a right angled triangle with one of its acute angle as \theta .

  • The side opposite to this angle will be perpendicular .
  • Also we know that ,

\sf\longrightarrow sin\theta =\dfrac{p}{h} \\

\sf\longrightarrow cos\theta =\dfrac{b}{h}

And by Pythagoras theorem ,

\sf\longrightarrow h^2 = p^2+b^2 \dots (i)

Where the symbols have their usual meaning.

Now , taking LHS ,

\sf\longrightarrow sin^2\theta +cos^2\theta

  • Substituting the respective values,

\sf\longrightarrow \bigg(\dfrac{p}{h}\bigg)^2+\bigg(\dfrac{b}{h}\bigg)^2\\

\sf\longrightarrow \dfrac{p^2}{h^2}+\dfrac{b^2}{h^2}\\

\sf\longrightarrow \dfrac{p^2+b^2}{h^2}

  • From equation (i) ,

\sf\longrightarrow\cancel{ \dfrac{h^2}{h^2}}\\

\sf\longrightarrow \bf 1 = RHS

Since LHS = RHS ,

Hence Proved !

I hope this helps.

You might be interested in
What is the value of y?
Slav-nsk [51]
In a triangle all of the angles always add up to 180, so let's set up an equation.

79 + 37 + y = 180
Simplify
116 + y = 180
Subtract 116 from both sides.
y = 64

The value of y is 64.

Hopefully this helps! If you have any more questions or don't understand, please comment or DM me, and I'll get back to you ASAP. :)
6 0
3 years ago
Which table represents a linear function? (Will give brainliest)
34kurt
Only this function is lineer.
Because it is arithmetic.

6 0
3 years ago
Read 2 more answers
What is the solution for 2y=x+2<br> x-3y=-5
Mars2501 [29]

Answer:

x = 4

y = 3

Step-by-step explanation:

<u>Given </u><u>equations </u><u>:</u><u>-</u>

  • 2y = x + 2
  • x - 3y = -5

<u>Second</u><u> </u><u>equation</u><u> </u><u>can </u><u>be</u><u> written</u><u> as</u><u> </u><u>,</u><u> </u>

  • x - 3y = -5
  • -3y = -x - 5

<u>Adding</u><u> </u><u>them </u><u>:</u><u>-</u><u> </u>

  • -3y + 2y = 2 -5
  • -y = -3
  • y = 3

<u>Put </u><u>this </u><u>in </u><u>(</u><u>ii)</u><u> </u><u>:</u><u>-</u><u> </u>

  • x = 3y - 5
  • x = 3*3 - 5
  • x = 9 -5
  • X = 4
8 0
2 years ago
Read 2 more answers
Which is the equation of the linear model?
Zielflug [23.3K]
The answer is B. y =  0.75 + 2.25. because i've done this assement.

3 0
3 years ago
{x | x is the reciprocal of a natural number}
Genrish500 [490]

Answer:

x∈(0,1], x is natural number.

8 0
3 years ago
Other questions:
  • Circle A is tangent to circle B.<br> True<br> False
    14·1 answer
  • Find the x- and y-intercept of the line. <br><br> 5x – 4y = 40
    14·1 answer
  • Your friend Bamey Fife was remodeling his kitchen. He went shopping for a new refrigerator. The salesman at AppliancesRUs showed
    13·1 answer
  • Model the expression -3 3/4 + 1/2 on a number line
    15·2 answers
  • The scale of a map is 1 1/4 inches = 100 miles. On the map, two rivers are 4 1/8 inches apart. What is the distance between the
    7·1 answer
  • What is the y-intercept of 2y=-3x+18
    14·2 answers
  • I need help ASAP will mark the brainliest
    13·2 answers
  • Please help got to get grade up
    9·1 answer
  • Each lap around the track takes Mike 3.5 minutes to walk.
    9·2 answers
  • After she graduated from college, Brianna began teaching at a salary of $28,750 a year. Which of the following choices shows Bri
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!