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If 4 tan theta=3 ,evaluate 4sin theta -cos theta 1/4 sin theta -cos theta-1?
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If 4 tan theta=3 ,evaluate 4sin theta -cos theta 1/4 sin theta -cos t...
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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(�)
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