The most straightforward way to obtain the expression for cos(2x) is by using the “cosine of the sum” formula: cos(x + y) = cosx*cosy – sinx*siny. cos(2x) = cos² (x) – (1 – cos²(x)) = 2cos²(x) – 1.

The derivative of tan 2x is 2 sec2 (2x). Was this answer helpful?

Write 1 as cos2x+sin2x and cos2x as cos2x−sin2x. Then sec2x=cos2x+sin2xcos2x−sin2x. Next, divide top and bottom (of the right hand side) by cos2x and use the fact that 1+tan2x=sec2x. You are then familiar with the identity cos(2x)=2cos2(x)−1.

If you want to get sec2(0), you should first notice that sec2(0)=1cos2(0). I would, then, first get cos(0), and then press the x^2 and 1/x buttons.

Therefore, 1 + cos2x = 2cos^2(x)…….

1. You can replace sin2 x with (1 – cos2 x) and simplify to get cos 2x = 2 cos2 x – 1.
2. You can replace cos2 x with (1 – sin2 x) and simplify to get cos 2x = 1 – 2 sin2 x.

Answer: The expression for cos 3x in terms of cos x is 4 cos3x – 3 cos x.

/sin 3x =4/sin x/sin(60^{/circ}-x)/sin(60^{/circ}+x).

To enter cos2x into your calculator, calculate cos x and square it. For an algebraic solution write y = cos x and then the equation becomes 2 y2 – 3 y – 4 = 0.

x=(n±14)π where n = 0, 1, 2. . . . . . . . Hence this is our required solution of cos2x = 0.

Answer: The formula of Sin3x is (3 sinx- sin3x)/4.

tan−1x = tan−1(x), sometimes interpreted as (tan(x))−1 = 1tan(x) = cot(x) or cotangent of x, the multiplicative inverse (or reciprocal) of the trigonometric function tangent (see above for ambiguity)

cot(x) = 1/tan(x) , so cotangent is basically the reciprocal of a tangent, or, in other words, the multiplicative inverse.

The inverse function of cotangent. Basic idea: To find cot-1 1, we ask “what angle has cotangent equal to 1?” The answer is 45°. As a result we say cot-1 1 = 45°….

Like the inverse of sin, the inverse of tan is also restricted to quadrants 1 and 4. Knowing this we are solving for the inverse of tan -1. We are basically being asked the question what angle/radian does tan(-1) equal. Using the unit circle we can see that tan(1)= pi/4.

Today we discuss the four other trigonometric functions: tangent, cotangent, secant, and cosecant. The tangent of x is defined to be its sine divided by its cosine: tan x = sin x cos x . The cotangent of x is defined to be the cosine of x divided by the sine of x: cot x = cos x sin x .

Inverse Trigonometric Formulas List

arcsec

Allied to these are the three reciprocal ratios, cosecant, secant and cotangent: cosecθ=hypotenuseopposite,secθ=hypotenuseadjacent,cotθ=adjacentopposite.