Solve the trigonometric equations. (a) 2cos (x) = V3 in [0, 2n) (b) tan(x)–1 = 0 in [0, 2n) (c) V2 sin(0) + 1 = 0 in (-∞, 0∞0) (d) sin(x) = 1 – 2cos²(x) in [0, 2n)

Q: (1) Prove sin(A+B) = sin(A) cos(B)+sin(B) cos(A) by using the formula for cos(A+B)and a cofunction…

A: Given:

Q: Prove the following identities: tan(v) + cot(v) (a) sec(v) csc(v) 1- sin(0) (b) cos(0) 1 SE cos(8)…

A:

Q: (3) Proving that sin?(x) + cos (x) = 1: d. (a) Show that -(cos² (x)+ sin (x)) = 0. What does the…

A:

Q: 6 sin(x) + 2 cos(x) = 0

A: We are given trigonometric equation as

Q: 15 sin2(x) − 22 sin(x) + 8 = 0

A: To solve the given equation

Q: Find the form for a particular solution to the equation y "+2y'– 3y =r?cos (nt). A…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: (a) Find all singularities of the function f(z): = sin cos(z-7) (z - 3T) (z+4i)²¹ and determine the…

A:

Q: sin(a)= 4/5 and cos (B)= -7/25.  Find sin(2a) and cos (a-B)  ,with pi/2<a<pi and pi<B<3pi/2

A:

Q: Give an example of a value of z such that the equation sin(x ) = z is unsolvable.

A: We have to give an example of a value of z such that the equation sinx=z is unsolvable.

Q: 4x? )(i) Use the substitution x= tan e to show that sin? 20 dx. %3D (1+x*)' 4x2 (ii) Hence find in…

A:

Q: 1– sin (t) 1 2 sec? (t) = + cos² (t) `1-sin (t)

A: To verify 2sec2t=1-sintcos2t+11-sint

Q: (a) Is Rolle's Theorem applies for the function f (x) = cos(sin-1x) on the closed interval [-1,1]?…

A:

Q: sin(x) - 4x° + (1+ x2}? Jdx =0

A: Topic- Definite integration of odd function

Q: sin(x) + cos(y) 1 + sin(x) cos(y).

A: Given query is to find the dy/dx at x = 0 and y = π/2

Q: (1) Given f(x) (a) Find f 1 1-x 2 (²). f(x) = 2 and g(x)=√x² +2. (b) Find fog (c) Find and simplify…

A:

Q: a) [(1-5x)dx x (x+1) b) dx c) dx 2/x x

A: Since you have posted question with multiple subparts we will solve the first three subparts for you…

Q: sin (0) cos(0) d0, cos (0) dө, u = sin(0)

A:

Q: State the sum and difference formulas for the cosine. cos (x + y) = cos (x) cos (y) - sin (y) sin(x)…

A:

Q: (1) sin (z + y) com ( z + v) (2) COS

A:

Q: An appropriate trigonometric substitution 1 -dx is V4 – x² for x = 2 tan(8) for 0 E (-5,5) а. b. x =…

A: The given integral is: ∫14-x2dx

Q: (3) Solve the equations for x and correct the answer to four decimal places. (a) 52-1 = 32+1 (b) 4…

A: Given Equations are as follows As we know that

Q: Verify the identity. (1 - sin?(t) + 3 cos²(t))2 + 16 sin?(t) cos?(t) = 16 cos?(t) (1 - sin?(t) + 3…

A: