Class 10 Exam > Class 10 Questions > If 4 tan theta=3 ,evaluate 4sin theta -cos th...
Start Learning for Free
If 4 tan theta=3 ,evaluate 4sin theta -cos theta 1/4 sin theta -cos theta-1?
Most Upvoted Answer
If 4 tan theta=3 ,evaluate 4sin theta -cos theta 1/4 sin theta -cos t...
Answer
Finding the value of sin(theta) and cos(theta)
We are given that 4 tan theta = 3. We can use the identity tan^2(theta) + 1 = sec^2(theta) to find the value of cos(theta) and sin(theta).
First, we can square both sides of the equation 4 tan theta = 3 to get:
16 tan^2 theta = 9
Then, we can substitute tan^2(theta) with sec^2(theta) - 1 to get:
16(sec^2(theta) - 1) = 9
Simplifying this equation, we get:
16 sec^2(theta) - 16 = 9
Adding 16 to both sides, we get:
16 sec^2(theta) = 25
Dividing both sides by 16, we get:
sec^2(theta) = 25/16
Taking the square root of both sides, we get:
sec(theta) = 5/4
Now, we can use the identity sec^2(theta) = 1/cos^2(theta) to find the value of cos(theta):
cos^2(theta) = 1/sec^2(theta)
cos^2(theta) = 16/25
cos(theta) = +/- 4/5
Since 4 tan(theta) = 3, we know that tan(theta) = 3/4. Using the identity tan^2(theta) + 1 = sec^2(theta), we can find the value of sin(theta):
tan^2(theta) + 1 = sec^2(theta)
(3/4)^2 + 1 = (5/4)^2
9/16 + 1 = 25/16
sin^2(theta) = 16/25
sin(theta) = +/- 4/5
Since cos(theta) and sin(theta) have opposite signs, we know that cos(theta) = -4/5 and sin(theta) = 3/5.
Finding the value of 4sin(theta) - cos(theta)
Now that we have found the values of sin(theta) and cos(theta), we can use them to evaluate the expression 4sin(theta) - cos(theta).
4sin(theta) - cos(theta) = 4(3/5) - (-4/5)
4sin(theta) - cos(theta) = 12/5 + 4/5
4sin(theta) - cos(theta) = 16/5
Finding the value of 1/4sin(theta) - cos(theta) - 1
Now we can use the value we found above to evaluate the expression 1/4sin(theta) - cos(theta) - 1.
Community Answer
If 4 tan theta=3 ,evaluate 4sin theta -cos theta 1/4 sin theta -cos t...
4 tan=3 since tan=3/4 now,
Tan=perpendicular/base
So,tan=3/4
Now,
Hypotenuse= root 3^+4^
=root 9+16
=root 25
=5
Using this we can find ,
Sin= perpendicular/hypotenuse =3/5
Cos=base/hypotenuse =4/5
A.C.T.P:
(4sin theta_ cos+1)/(4sin theta+ cos_1)
=(4�3/5_4/5+1)/(4�3/5+4/5_1)
= (12_4+5)/(12+4_5)
=13/11
In place of question mark keep multiplication symbol(�)
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
If 4 tan theta=3 ,evaluate 4sin theta -cos theta 1/4 sin theta -cos theta-1?
Question Description
If 4 tan theta=3 ,evaluate 4sin theta -cos theta 1/4 sin theta -cos theta-1? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If 4 tan theta=3 ,evaluate 4sin theta -cos theta 1/4 sin theta -cos theta-1? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 4 tan theta=3 ,evaluate 4sin theta -cos theta 1/4 sin theta -cos theta-1?.
If 4 tan theta=3 ,evaluate 4sin theta -cos theta 1/4 sin theta -cos theta-1? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If 4 tan theta=3 ,evaluate 4sin theta -cos theta 1/4 sin theta -cos theta-1? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 4 tan theta=3 ,evaluate 4sin theta -cos theta 1/4 sin theta -cos theta-1?.
Solutions for If 4 tan theta=3 ,evaluate 4sin theta -cos theta 1/4 sin theta -cos theta-1? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of If 4 tan theta=3 ,evaluate 4sin theta -cos theta 1/4 sin theta -cos theta-1? defined & explained in the simplest way possible. Besides giving the explanation of
If 4 tan theta=3 ,evaluate 4sin theta -cos theta 1/4 sin theta -cos theta-1?, a detailed solution for If 4 tan theta=3 ,evaluate 4sin theta -cos theta 1/4 sin theta -cos theta-1? has been provided alongside types of If 4 tan theta=3 ,evaluate 4sin theta -cos theta 1/4 sin theta -cos theta-1? theory, EduRev gives you an
ample number of questions to practice If 4 tan theta=3 ,evaluate 4sin theta -cos theta 1/4 sin theta -cos theta-1? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup