Verify that the following expression is an identity by simplifying one side of the equation to equal the other side. cot(x) + tan(x) = sec(x) csc(x)

Q: If x > 0, write sec(tan-1 x) as an algebraic expression in x.

A: Now let

Q: Write sin(3x) cos(7x) as a sum of trigonometric functions.

A: Given trigonometric function is  sin3x cos7x. Write the sin3x cos7x as a sum of trigonometric…

Q: Determine if each equation is an identity by graphing each side v sin² (x)+cos² (x) sin(x) csc (x)…

A: An identity is an equation which is satisfied for all 'x' values in the domain.

Q: Simplify sin(arccos (G) arctan x) by writing it as a simplified algebraic expression.

A: The detailed explanation is given as below-

Q: sec" (*) 1 - tan?(x) cos? (x) %3D sin(x) + sin(x) sin“ (æ) – cos“ (x) = -

A:

Q: What is the meaning of the notation y = tan-1 x?

A: Given: y=tan-1x We know the meaning of following notation: sin-1x sine inverse x cos-1x cosine…

Q: Write the exact form:  sec(2x) if sin(x)=2/5

A: We need to evaluate the value of sec2x if sinx = 25

Q: simplify: csc(x)-cos(x)cot(x)

A: simplify: cscx-cosxcotx

Q: Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if…

A:

Q: 5) cos X = 35 B. 12 37 R

A: Use the trigonometry ratio formula for cosx

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.