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
Katen [24]
3 years ago
14

Please someone help me. It's about proving related to transformation of trigonometric ratios. Thank you!!​

Mathematics
2 answers:
gtnhenbr [62]3 years ago
6 0

Answer:    see proof below

<u>Step-by-step explanation:</u>

* Use the following Co-function Identity: sin A = cos(90 - A)

* Use the following Sum to Product Identities:

 cos x - cos y = 2 sin [(x + y)/2] · sin [(x - y)/2]

 cos x + cos y = 2 cos [(x + y)/2] · cos [(x - y)/2]

* Use the Unit Circle to evaluate cos 45 = sin 45 = √2/2

<u>Proof LHS → RHS</u>

\text{LHS:}\qquad \qquad \qquad \qquad \quad \dfrac{\cos 10-\sin 10}{\cos 10+\sin 10}\\\\\\\text{Co-function Identity:}\qquad \dfrac{\cos 10 -\cos (90-10)}{\cos 10+\cos (90-10)}\\\\\\\text{Product to Sum Identity:}\quad \dfrac{2\sin (\frac{10+80}{2})\sin (\frac{80-10}{2})}{2\cos (\frac{10+80}{2})\cos (\frac{80-10}{2})}\\\\\\\text{Simplify:}\qquad \qquad \qquad \qquad \dfrac{2\sin (45)\sin (35)}{2 \cos (45)\cos (35)}

.\qquad \qquad \qquad \qquad \qquad = \dfrac{2(\frac{\sqrt2}{2}) \sin (35)}{2(\frac{\sqrt2}{2}) \cos(35)}\\\\\\.\qquad \qquad \qquad \qquad \qquad = \tan (35)

LHS = RHS:   tan 35 = tan 35   \checkmark

kvasek [131]3 years ago
5 0

Answer:

see explanation

Step-by-step explanation:

Using sum to product identities

cos x - cos y = - 2sin(\frac{x+y}{2} )sin(\frac{x-y}{2} ) = 2sin(\frac{x+y}{2} )sin(\frac{y-x}{2} )

cos x + cos y = 2cos(\frac{x+y}{2} )cos(\frac{x-y}{2} )

Note that

sin10° = sin(90 - 10)° = cos80°

Thus

\frac{2sin(\frac{10+80}{2})sin(\frac{80-10}{2})  }{2cos(\frac{10+80}{2})cos(\frac{80-10}{2})  } ← cancel 2 from numerator/ denominator

= \frac{sin45}{cos45} × \frac{sin35}{cos35}

= tan45° × tan35° { tan45° = 1 ]

= 1 × tan35°

= tan35° ← as required

You might be interested in
What should I put for x in the box? first to answer is brainliest
aleksklad [387]

Answer:

x=-1, x= 1

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
15 books each of dimension 2 cm x 4 cm x 5 cm are stacked on a she
Elena L [17]

Answer:

30cm

Step-by-step explanation:

Assuming that the thickness of the books is 2cm (This is a reasonable assumption, as books are almost always longer and wider than they are thick, and assuming that the books are stacked flat on top of one another, faces up or down, and not sideways, the question becomes 'What is the height of 15 books stacked on top of one another, if each book is 2cm thick?' The answer to this question is 15*2 or 30.

7 0
3 years ago
Read 2 more answers
The formula for the area of a rectangular piece of paper is , where is the length and is the width of the piece of paper. What i
Andreyy89

Step-by-step explanation:

you multiply the length time the width

the answer would be in cm^2

7 0
3 years ago
Estimate the perimeter of the figure to the nearest whole number.
Marat540 [252]

Answer:

the answer is 19.3137

Step-by-step explanation:

each of the diagonal lines are 2.84 so multiply that times 4 because there are 4 of them then add the top and bottom lines which are 4 each so 8 plus the diagonal lines which are 11.3137 and you get 19.3137.

7 0
4 years ago
Read 2 more answers
Ben solved an equation as shown below, Equation 2 (-3×+1)=9×-8. what did he do wrong. step1. -6×+2=9×- 8. step2. -6×+9×=-8+2. st
AlekseyPX
He just switched sides of the variables and numbers. Instead if adding the opposite.
8 0
4 years ago
Read 2 more answers
Other questions:
  • What is the range of values for the measurement 500±4%
    9·1 answer
  • Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) −
    10·1 answer
  • The height of the Empire State Building is 318.00 meters. If a stone is dropped from the top of the building, what is the stone'
    9·1 answer
  • What is the Golden Ratio?
    9·2 answers
  • The store ordered small posters and large posters to promote their opening 12 times as many small posters were ordered as large
    10·2 answers
  • Scott took out a 4-year car loan for $5,500. He paid back a total of $7,370. What interest rate did he pay for this loan?
    8·1 answer
  • If you place a 20ft ladder 4ft from the base of the wall, what is the angle measure of the ladder to the ground to the nearest d
    10·1 answer
  • Select the correct answer.
    9·2 answers
  • Write the slope intercept form of the equation that formed this line when graphed
    11·1 answer
  • Can anyone help find the measurement pls ty
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!