Question: a) Use the identity sin x + cos x = 1 to prove that b) Use the identity you proved in part (a) to find

a) Use the identity sin² x + cos² x = 1 to prove that

1+ sinx cos.x cosx = tanx + tanx + 1.


b) Use the identity you proved in part (a) to find the minimum values of

1+ sinx cos.x cosx = tanx + tanx + 1.

Step by Step Solution

★★★★★

3.32 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

ANSWER a Starting with the lefthand side of the given equation 1 sin x cos xcos2 x cos2 x cos2 x sin ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Complete Pure Mathematics Questions!

Q:

In a situation where capital is more represented on the side of permanent and long-term capital and less long-term provisions and long-term liabilities maintenance of financial stability is: a)...

Q:

a. Use the identity sin (a + h) = sin a cos h + cos a sin h with the fact that to prove that thereby establishing that sin x is continuous for all x. (Hint: Let h = x - a so that x = a + h and note...

Q:

In Exercises 1 and 2, compute the area of the triangle with the given vertices using both methods. 1. A = (1, - 1), B = (2, 2), C = (4, 0) 2. A = (3, - 1, 4), B = (4, -2, 6), C = (5, 0, 2) Figure 1...

Q:

18. Find the equation for a line which passes through the points (1, 7) and (3,1). . Write the equation in slope-intercept form. Show work. 19. Find the exact solutions and simplify as much as...

Q:

This is Calculus and vector course for grade 12 high school. Those are the questions I need help with and I also attached photo of formula sheet in case you need it as a reference. Those are three...

Q:

Prove the identity sin x cos x 1 sin 2x Expand the product and use a Pythagorean Identity and a Double Angle Formula to simplify sin x cos x sin x 2 sin x cos x 1 2 sin x

Q:

24 . Prove the identity (sin x cos x)2 = 1 sin 2x 25. From a point 47 feet from the base of a redwood tree, the angle of elevation to the top of the tree is 54.3\". Find the height of the tree to the...

Q:

1. (10 pts) Find a, b, and c for the function f(x) = asin(bx + c) such that the graph of f matches the figure. -3+ 2. (20 pts) Find the exact value of the following expression. (a) arccos cos 2" )...

Q:

ii. Make use of the trig identity sin x + cos x = 1 in your equation you found in part (i). You should arrive at an equation involving cos(x)dx and cos (x)dx. Solve this equation for cos(x)dx in...

Q:

Develop the parametric equations of a hyperbola by following these steps. a. Write the equation of a unit hyperbola in standard form using x and y. b. Replace x with 1 / cos t and solve for y in...

Q:

Write a script that plays the guess the number. Choose the number to be guessed by selecting a random integer in the range 1 to 1000 Do not reveal this number to the user. Display the prompt Guess my...

Q:

Dace Company manufactures two products. Product F and Product G. The company expects to produce and sell 1,900 units of Product F and 6,000 units of Product G during the current year. The company...

Q:

4.37 A dealers profit, in units of $5000, on a new automobile is a random variable X having the density function given in Exercise 4.12 on page 137. Find the variance of X.

Q:

2 Reload the result of Exercise 4.4 and apply the written PRP in order to generate the total differential expansion of (4.1) based on definition (4.6) of [18]. Visualize the Karnaugh map of the...

Q:

Assess whether there is a relationship between BMD at the femoral neck and cigarette smoking using CI methodology?

Q:

Assess whether there is a relationship between BMD at the femoral shaft and cigarette smoking using CI methodology?

Q:

Using the computer, generate 200 random samples from a binomial distribution with n = 10 and p = .6. Derive a large sample two-sided 90% CI for p based on each sample?

Q:

CyclePath Company produces two different products that have the following price and cost characteristics. Management believes that pushing sales of the Bicycle product would maximize company profits...

Q:

Question:51 Freezing Limited intends to bid-for-a-contract to manufacture a customised-fridge-for-Winter- Limited. The details of the special order are as follows: 1 (a)-The company purchased...

Q:

On December 3 1 , Year 2 , Palm Inc. purchased 8 0 % of the outstanding ordinary shares of Storm Company for $ 4 2 0 , 0 0 0 . At that date, Storm had ordinary shares of $ 3 1 0 , 0 0 0 and retained...