See full process below. Let 2tan^-1 (1/5)+tan^-1 (1/7)+2tan^-1 (1/8)=a Let theta=tan^-1 (1/5) and phi=tan^-1 (1/7) and psi=tan^-1 (1/8) Then tantheta=1/5 and tanphi=1 ...
How do you prove that 2\tan ^ { - 1} \frac { 1} { 5} + \tan ^ { - 1 ...
Let z=x+pi/4 So tanz=tan (x+pi/4) =>tanz= (tanx+tan (pi/4))/ (1-tanxtan (pi/4)) =>tanz= (tanx+1)/ (1-tanx) =>tanz= (2+1)/ (1-2)=-3 So zin "quadrant II or IV" Now cotz ...
If Tan(x) = 2, and 0 < x < 2pi, find the exact value of Sin(x + pi/4 ...
Explanation: Use the trig identity: #tan (a + b) = (tan a + tan b)/ (1 - tan a.tan b)# Call t = (x/2) and develop the left side #LS = tan (t + pi/4) = (tan t + tan ...
Explanation: #tan^2x+ (sqrt (3)-1)tanx-sqrt (3)=0# Let #u=tanx# #u^2+ (sqrt (3)-1)u-sqrt (3)=0# Factor: # (u-1) (u+sqrt (3))=0=>u=1, and u=-sqrt (3)# But #u=tanx#
How can I solve this? tan^2 x + (√3-1)tan x -√3 =0 - Socratic
To prove that an equation is not an identity and, therefore, cannot be proven, it is sufficient to find one value of x where the left side does not equal the right side. Given: 2tan(x)/sin^2(x) = sec^2(x) Let x = pi/4 2tan(pi/4)/sin^2(pi/4) = sec^2(pi/4) Substitute tan(pi/4) = 1, sin^2(pi/4) = 1/2 and sec^2(pi/4) = 2 2 1/(1/2) = 2 4 != 2 This proves that the equation 2tan(x)/sin^2(x) = sec^2(x ...
The equation may be written as tan^2beta - tanbeta = 0 or tan beta * (tan beta - 1) = 0 Hence tanbeta = 0 or (tanbeta - 1) = 0 If tanbeta = 0 then beta = npi, where n = 0,1,2 . . .etc Or if tanbeta - 1 = 0 then tan beta = 1 or beta = pi / 4 + n * pi