Write each expression as an equivalent algebraic expression involving only x. (Assume xis positive.)   sin (2 cos-1 x)

Q: cos 0 1- 1+sin0

A: To simplify.

Q: Write each expression as an equivalent algebraic expression involving only x. (Assume xis positive.)…

A: Given: sin2tan-1x for solving this we assume tan-1x=θ and use formula sin2x=2sinxcosx so, tanθ=x…

Q: 2 16 sin *x cos x

A: Given, the expression 8sin2xcos2x. We have to write this expression in terms of trignometric…

Q: Write the following expression in terms of sine and cosine, and simplify it. (The final expression…

A: We use Trigonometry identities

Q: Simplify the expression as much as possible. 1 - cos(-x) sinx + sinx 1 - cos(-x)

A: Topic - Simplification of trigonometric expression We are given, 1-cos(-x)sin x+sin x1-cos(-x)We…

Q: Write an equivalent algebraic expression that involves x only.      tan (cos- 1 x)

A: Evaluate tancos-1x       ...(1)

Q: Rewrite the expression as an algebraic expression in x. tan(sin-1(x))

A:

Q: Simplify the expression.

A: Given: The expression cscθ+11sin2θ+cscθ, To find: The simplified expression of the given expression.

Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.