cos square there + cos square theta multiply cot square theta = cot square theta​

Answers

Answer 1

Explanation:

We need to prove that : [tex]\cos^2\theta+\cos^2\theta {\cdot} \cot^2\theta=\cot^2\theta[/tex]

Taking LHS : [tex]\cos^2\theta+\cos^2\theta {\cdot} \cot^2\theta[/tex]

Taking [tex]\cos^2\theta[/tex] common as follows :

[tex]\cos^2\theta(1+ \cot^2\theta)[/tex] ...(1)

We know that :

[tex]cosec^2\theta-\cot^2\theta=1\\\\cosec^2\theta=1+\cos^2\theta[/tex] ....(2)

Use equation (2) in equation (1) as follows :

[tex]\cos^2\theta{\cdot} cosec^2\theta[/tex]

We know that : [tex]cosec\theta=\dfrac{1}{\sin\theta}[/tex]

So,

[tex]\cos^2\theta{\cdot} \dfrac{1}{\sin^2\theta}\\\\=\cot^2\theta[/tex]

=RHS

Hence, LHS = RHS


Related Questions

Other Questions
With a planned volume of 15,000 units, the master budget includes variable costs of $450,000 and fixed costs of $350,000. If the actual volume is 12,000 units, the total costs under flexible budget should be:__________a. $490,000.b. $560,000.c. $650,000.d. $710,000. y'all don't have to answer this I got it:) Dry ice is a form of carbon dioxide that sublimates at room temperature. At a Halloween party, some students noticed that the dry ice underwent a phase change. Which statement below best describes the change in the energy and physical characteristics of the molecules of carbon dioxide during this process?a: The molecules experienced a physical change from a gaseous state to a liquid state, releasing energy into the environment and reducing the molecular movement.b: The molecules experienced a chemical change as the carbon dioxide reacted with oxygen, which released oxygen gas into the environment and increased the molecular movement.c: The molecules experienced a physical change from a solid state to a gaseous state, which increased the molecular movement and the energy of the carbon dioxide molecules. d: The molecules experienced a chemical change from a liquid state to a solid state, which reduced the amount of energy between the carbon dioxide molecules and decreased the molecular movement. 3. Which statement best expresses a theme in the poem? A. A strong support system is necessary to overcome adversity. B. Gaining confidence with a new task requires independence and attention to detail. C. It takes time and courage to endure unfamiliar circumstances. D. Friends can inspire us to embrace the mystery of the unknown. draw a graph of y equals 7 + 4 x - 2x squared a) use a graph to find the Turning point b) use your graph to look for the roots . *5O POINTS, BE FAST!!!!!*100 words Essay in English on "Can't Time Come Back?" Please help me it due today at 11:59pm please help me will mark the brainiest please [Choose ]Yo soy Carla; yo tengo el pelo castao.Yo soy Juan y soy rubio.Me llamo Susan y soy baja.Arthur, t tienes el pelo castao. What is the role of CdKs? to create enzymes that produce chemical changes to signal the cell to move to the next phase of the cell cycle to build structural components of DNA and energy-rich substances to activate the cyclins that cause progression of the cell cycle Nina can stitch 3 of a dress in 4 hours. If drepresents the number of dresses and h represents the number of hours, which equationrepresents this proportional relationship?OA d=6B.3d=4hoc. d = 13hD.d=4OE. d=12 I really need some help on this What rules existed in the household? What rights did women have in the Roman Republic? ) Multiply (x 4)(x2 5x 6). x3 9x2 + 14x + 24 x3 x2 + 26x + 24 x3 5x2 + 10x + 24 x3 15x2 + 20x + 24 Question 10(Multiple Choice Worth 6 points) (01.03 MC) Solve for all possible values of x. square root of the quantity x minus 8 end quantity minus 3 equals 1 x = 4 x = 8 x = 12 x = 24 A ceiling light made out of abstract pieces of blown glass extending in all directions from the center of the light.What is the picture above an example of? How was this piece, and others similar, made? quin puede ayudarme a aprender espaol? 100 writen as a perfect square Gabriella, a single taxpayer, has wage income of $160,000. In addition, she has $7,000 in long-term capital losses, $1,000 in long-term capital gains, $3,000 in short-term capital gains, and $1,000 in short-term losses. What is Gabriella's AGI for 2017?a. $157,000.b. $160,000.c. $156,000.d. $161,000. Differentiation means that:_________ a. the firm should aim its efforts at a target market that is different from a target market that a competitor would find attractive. b. a firm's marketing mix is distinct from and better than what is available from a competitor. c. a firm uses its resources in a different way than competitors use their resources. d. a firm should screen out opportunities using different criteria than those used by other firms. e. when a firm's marketing strategy is not going well it should change to a different set of operational decisions. Stefan is reading scientific articles and research reports to answer his research question for a paper. What should Stefan do when he encounters scientific words in the texts?A)Find out the meanings of most of the scientific words in all the articles.B)Guess at the meanings of the scientific words he doesnt know.C) Learn the precise meanings of the scientific words that apply to his topic.D) Memorize the precise meanings of all scientific words in all the articles. Which theoretical perspective views the family as a living thing, with each component influencing all of the others?