1. solve tan36 degrees- tan2degrees/ 1+tan36 degrees tan 2 degrees as a single function.
2. Find the exact value of sin (α-β) if sina=4/5 and cos β= -9/41 terminal side of α lies in I and terminal side of β lies in III
3. If cosx=1/12 and sinx > 0, find tan2x
thankyou!
1. tan(36 - 2) = tan 34
2. sin ? = 4/5 --> cos ? = 3/5
cos ? = -9/41 --> sin ? = -40/41
sin(?-?) = sin?*cos? - cos?*sin? = ?
3. tan x = sqrt(143)
tan 2x = 2tanx/(1 - tan^2(x)) = ?
how to calculate the value of tan36°
1. To solve the given expression tan36 degrees - tan2 degrees / (1 + tan36 degrees * tan2 degrees) as a single function, we can make use of the trigonometric identity: tan(A - B) = (tanA - tanB) / (1 + tanA * tanB).
In this case, A = 36 degrees and B = 2 degrees.
So we need to find tan(36 degrees - 2 degrees) as a single function.
First, calculate the values of tan(36 degrees) and tan(2 degrees) using a calculator.
Next, substitute these values into the above trigonometric identity:
tan(36 degrees - 2 degrees) = (tan(36 degrees) - tan(2 degrees)) / (1 + tan(36 degrees) * tan(2 degrees))
Finally, simplify the expression to get the single function.
2. To find the exact value of sin(α - β) given sina = 4/5 and cos β = -9/41, we will use the trigonometric identity: sin(α - β) = sinα cosβ - cosα sinβ.
Here, we are given sina = 4/5 and cos β = -9/41.
Using the Pythagorean identity sin^2 β + cos^2 β = 1, we can find sin β:
cos^2 β = 1 - sin^2 β
(-9/41)^2 = 1 - sin^2 β
sin^2 β = 1 - (-9/41)^2
sin β = √(1 - (-9/41)^2)
Also, since sina = 4/5, we know cosα = √(1 - sina^2):
cosα = √(1 - (4/5)^2)
Now we can substitute these values into the trigonometric identity:
sin(α - β) = (4/5)(-9/41) - √(1 - (4/5)^2)√(1 - (-9/41)^2)
Simplify the expression to get the exact value of sin(α - β).
3. Given cosx = 1/12 and sinx > 0, we can find tan2x using the trigonometric identity: tan2x = (2tanx) / (1 - tan^2x).
Here, we are given cosx = 1/12. Using the Pythagorean identity sin^2 x + cos^2 x = 1, we can find sinx:
sin^2 x = 1 - cos^2 x
sin^2 x = 1 - (1/12)^2
sin x = √(1 - (1/12)^2)
Now we can substitute these values into the trigonometric identity:
tan2x = (2tanx) / (1 - tan^2x)
tan2x = (2sinx/cosx) / (1 - (sinx/cosx)^2)
Simplify the expression to find tan2x.