Instead, think that the tangent of an angle in the unit circle is the slope If you pick a point on the circle then the slope will be its y coordinate over its x coordinate, ie y/x So at point (1, 0) at 0° then the tan = y/x = 0/1 = 0 At 45° or pi/4, we are at an x, y of (√2/2, √2/2) and y / x for those weird numbers is 1 so tan 45As we know, from trigonometry identities, 1tan 2 A = sec 2 A sec 2 A – 1 = tan 2 A (1/cos 2 A) 1 = tan 2 A Putting the value of cos A = ⅘ (5/4) 2 – 1 = tan 2 A tan 2 A = 9/16 tan A = 3/4Now, using the trigonometric identity 1tan 2 a = sec 2 a sec 2 A = 1 (3/4) 2 sec 2 A = 25/16 sec A = ±5/4 Since, the ratio of lengths is positive, we can neglect sec A = 5/4 Therefore, sec A = 5/4 Example 2 (1 – sin A)/(1 sin A) = (sec A – tan A) 2 Solution Let us take the Left hand side of the equation LHS = (1 – sin A)/(1 sin A)
Trig Identity Sec 4x Tan 4x 1 2tan 2x Youtube