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
prohojiy [21]
2 years ago
14

If 13cos theta -5=0 find sin theta +cos theta / sin theta -cos theta​

Mathematics
1 answer:
Ivahew [28]2 years ago
6 0

Step-by-step explanation:

<h3>Need to FinD :</h3>

  • We have to find the value of (sinθ + cosθ)/(sinθ - cosθ), when 13 cosθ - 5 = 0.

\red{\frak{Given}} \begin{cases} & \sf {13\ cos \theta\ -\ 5\ =\ 0\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \big\lgroup Can\ also\ be\ written\ as \big\rgroup} \\ & \sf {cos \theta\ =\ {\footnotesize{\dfrac{5}{13}}}} \end{cases}

Here, we're asked to find out the value of (sinθ + cosθ)/(sinθ - cosθ), when 13 cosθ - 5 = 0. In order to find the solution we're gonna use trigonometric ratios to find the value of sinθ and cosθ. Let us consider, a right angled triangle, say PQR.

Where,

  • PQ = Opposite side
  • QR = Adjacent side
  • RP = Hypotenuse
  • ∠Q = 90°
  • ∠C = θ

As we know that, 13 cosθ - 5 = 0 which is stated in the question. So, it can also be written as cosθ = 5/13. As per the cosine ratio, we know that,

\rightarrow {\underline{\boxed{\red{\sf{cos \theta\ =\ \dfrac{Adjacent\ side}{Hypotenuse}}}}}}

Since, we know that,

  • cosθ = 5/13
  • QR (Adjacent side) = 5
  • RP (Hypotenuse) = 13

So, we will find the PQ (Opposite side) in order to estimate the value of sinθ. So, by using the Pythagoras Theorem, we will find the PQ.

Therefore,

\red \bigstar {\underline{\underline{\pmb{\sf{According\ to\ Question:-}}}}}

\rule{200}{3}

\sf \dashrightarrow {(PQ)^2\ +\ (QR)^2\ =\ (RP)^2} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ +\ (5)^2\ =\ (13)^2} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ +\ 25\ =\ 169} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ =\ 169\ -\ 25} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ =\ 144} \\ \\ \\ \sf \dashrightarrow {PQ\ =\ \sqrt{144}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{PQ\ (Opposite\ side)\ =\ 12}}}}_{\sf \blue{\tiny{Required\ value}}}}

∴ Hence, the value of PQ (Opposite side) is 12. Now, in order to determine it's value, we will use the sine ratio.

\rightarrow {\underline{\boxed{\red{\sf{sin \theta\ =\ \dfrac{Opposite\ side}{Hypotenuse}}}}}}

Where,

  • Opposite side = 12
  • Hypotenuse = 13

Therefore,

\sf \rightarrow {sin \theta\ =\ \dfrac{12}{13}}

Now, we have the values of sinθ and cosθ, that are 12/13 and 5/13 respectively. Now, finally we will find out the value of the following.

\rightarrow {\underline{\boxed{\red{\sf{\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}}}}}}

  • By substituting the values, we get,

\rule{200}{3}

\sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ {\footnotesize{\dfrac{\Big( \dfrac{12}{13}\ +\ \dfrac{5}{13} \Big)}{\Big( \dfrac{12}{13}\ -\ \dfrac{5}{13} \Big)}}}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ {\footnotesize{\dfrac{\dfrac{17}{13}}{\dfrac{7}{13}}}}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{13} \times \dfrac{13}{7}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{\cancel{13}} \times \dfrac{\cancel{13}}{7}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{7}}}}}_{\sf \blue{\tiny{Required\ value}}}}

∴ Hence, the required answer is 17/7.

You might be interested in
Type the ordered pair that is the solution to these questions. <br> 3x-y=13
Dvinal [7]

Answer:

Here's 3 ordered pairs:

(0,-13)(1,-10)(2,-7)

Step-by-step explanation:

They should all be correct. It doesn't matter which one you choose.

3 0
3 years ago
Please help me asap!!!
Westkost [7]

Answer: immma guess that its c

super sorry if im wrong

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
What kind of triangle is this? 17 17 17
8_murik_8 [283]

Equilateral triangle. because all sides are equal.

7 0
3 years ago
Read 2 more answers
What is the reciprocal of<br> 8/5
azamat

Answer:

0.025

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
A = bh/2 solve for b
rjkz [21]
A =  \dfrac{bh}{2}

Cross multiply:
2A = bh

Divide by h on both sides:
b =  \dfrac{2A}{h}
8 0
3 years ago
Other questions:
  • Find the y-intercept and x-intercept of the line.
    7·2 answers
  • Which congruency theorem can be used to prove that △GHL ≅ △KHJ?
    13·2 answers
  • PLEASEE HELP ASAP I REALLY NEED HELP
    14·1 answer
  • Fred is making a fruit salad the ratio of cups of peaches to cups of cherries is 2:3 how many cups of peaches will feed need to
    13·1 answer
  • what are the coordinates of a point on the directed line segment from (5,9) to (8,-6) that partitions the segment into a ratio o
    6·1 answer
  • A circular swimming pool is 21 feet in diameter. What is the circumference
    13·1 answer
  • In the diagram below AB is parallel to CD what is the value of x
    13·1 answer
  • Which point is best represented by the ordered pair (2, -5.5)?
    15·2 answers
  • I would like to know what part of the ax+bx=c standard equation means in a graph
    8·1 answer
  • HELPPPPPPPPPPPPPPPPPPPPFind m
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!