Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation cos – 1 (x) – 2 sin – 1 (x) = cos – 1 (2 x) is equal to Open in App Solution Answer: ∫ Sin5x.dx = − 1 5.Sin4x.Cosx− 3Cosx 5 + Cos3x 15 ∫ S i n 5 x. d x = − 1 5. S i n 4 x. C o s x − 3 C o s x 5 + C o s 3 x 15. Example 2: Evaluate the integral of x3Log2x. Solution: Applying the reduction formula we can conveniently find the integral of the given expression. Below are some inverse tan properties and formulas that will help solve the problems of multiple-angle in Terms of tan-1 (X). tan (tan-1x) = x, for all real numbers x. tan-1 (tan x) = x, only when x ∈ R – {x: x = (2n + 1) (π/2), where n ∈ Z}. i.e., tan-1 (tan x) = x only when x is NOT an odd multiple of π/2. Otherwise, tan-1 (tan x) is Join Teachoo Black. Derivative of 〖𝒄𝒐𝒔𝒆𝒄〗^ (−𝟏) 𝒙 𝑓 (𝑥)=〖𝑐𝑜𝑠𝑒𝑐〗^ (−1) 𝑥 Let 𝒚= 〖𝒄𝒐𝒔𝒆𝒄〗^ (−𝟏) 𝒙 cosec⁡〖𝑦=𝑥〗 𝒙=𝐜𝐨𝐬𝐞𝐜⁡〖𝒚 〗 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑𝑥/𝑑𝑥 = (𝑑 (cosec⁡𝑦 ))/𝑑𝑥 1 Cot Inverse x is an inverse trigonometric function that gives the measure of the angle in radians or degrees corresponding to the value of x. Mathematically, it is written as cot -1 x or arccot x, pronounced as 'cot inverse x' and ' arc cot x', respectively. If a function f is invertible and its inverse is f -1, then we have f (x) = y ⇒ x = f The inverse trigonometric functions are also known as the anti trigonometric functions or arcus functions. The inverse trigonometric functions of sine, cosine, tangent, cosecant, secant, and cotangent are used to find the angle of a triangle from any of the trigonometric functions. It is widely used in many fields like geometry, engineering Finding the nthroots of a number using DeMoivre’s Theorem Example: Find all the complex fourth roots of 4. That is, nd all the complex solutions of G2owHQ7.

sin 1x cos 1x formula