Find value of tan75/2
15-8√3
Tan75/2
75/2
Tan75/2=?
To find the value of tan(75°/2), we can use the half-angle formula for tangent. The half-angle formula for tangent states that:
tan(x/2) = ±√((1-cosx)/(1+cosx))
We can substitute x with 75° in the formula to solve for tan(75°/2).
Step 1: Calculate cos(75°)
To find cos(75°), we can use the trigonometric identity, cos(a - b) = cosacosb + sinasinb. In this case, a = 30° and b = 45°.
cos(75°) = cos(30° + 45°)
= cos(30°)cos(45°) - sin(30°)sin(45°)
= (√3/2)(√2/2) - (1/2)(√2/2)
= (√6/4) - (√2/4)
= (√6 - √2)/4
Step 2: Substitute cos(75°) into the half-angle formula
Now, substitute cos(75°) into the half-angle formula for tangent:
tan(75°/2) = ±√((1 - cos75°)/(1 + cos75°))
= ±√((1 - (√6 - √2)/4)/(1 + (√6 - √2)/4))
By simplifying the expression, we can find the value of tan(75°/2).
Bindu (1,4)tatha (5,8)ke madh bindu ko mulbindu se milane vali rekh ka samikard geyt karo
(Root2-root3)(root2+1)
15root over3
If you mean tan(75/2), then
sin215 = (1+cos30)/2 = (2-√3)/4
cos215 = (1-cos30)/2 = (2+√3)/4
sin75 = cos15
cos75 = sin15
tan 75/2 = (1-cos75)/sin75
= (1 - √(2-√3)/4)/√((2+√3)/4)
= (2 - √(2 - √3))/√(2 + √3)
= 0.7673