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  • 3 answers

Arpit Mishra 4 years, 7 months ago

TanA+TanB/1-TanA×TanB

Anup Yadav 4 years, 8 months ago

TanA+TanB/1-tanA.tanB

Vikash Verma 4 years, 8 months ago

Tan(a)+tan(b) /1-tan(a)tan(b)
  • 1 answers

Gaurav Seth 4 years, 8 months ago

Given:

tan x = 1/7

tan y = 1/3

To Prove: cos 2x = sin 4y

We know that 

tan x = opposite / adjacent = 1/7

So using these value in right angle triangle ABC and Pythagoras theorem,

AC² = 1² + 7² = 1 + 49 = 50

AC = √50 = 5√2

⇒ sin x = opposite/hypotenuse = 1/5√2

⇒ cos x = adjacent/hypotenuse = 7/5√2

Also,

tan y = opposite / adjacent = 1/3

So using these value in right angle triangle LMN and Pythagoras theorem,

AC² = 1² + 3² = 1 + 9 = 10

AC = √10

⇒ sin y = opposite/hypotenuse = 1/√10

⇒ cos y = adjacent/hypotenuse = 3/√10

Now,

LHS = cos 2x = 2cos² x -1 = 2(7/5√2)² - 1 = 2(49/50) - 1

        = 24/25

RHS = sin 4y = 2 sin 2y cos 2y

        = 4 sin y cos y (2cos² y -1)

        = 4 (1/√10)(3/√10) ( 2(3/√10)² - 1 ) 

        = (12/10) ( 9/5 - 1 ) 

        = (6/5) ( 4/5 ) 

        = 24/25

LHS = RHS 

Hence proved.

 

  • 1 answers

Genius Boy 4 years, 7 months ago

A well defined collection of elements is called sets.
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Surya Vidhayak 3 years, 2 months ago

A+B-2AB

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A^2+B^2+2AB
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Varun Mishra 4 years, 8 months ago

sin3A= 3sinA-4sin^3A

Dipak Kumar 4 years, 8 months ago

Apana whatsapp n. De do

Vishal Maheshwari 4 years, 9 months ago

Sir mai class 11 mai ka student hu michhai maths ka simple paper chahiye sir
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Varun Mishra 4 years, 8 months ago

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Mayank Sharma 4 years, 9 months ago

my whats app no.9058213814= jo khuch ask karna hai mujhse whatsapp per phuchmy lo
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my whatsapp no.9058213814
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YouTube pr download kro
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Dipak Kumar 4 years, 8 months ago

Bhai playstor par jao aur 'ncrt math salutation in hindi' sarch karo
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Akhilesh Kumar 5 years ago

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Nitish Kumar 5 years ago

Fzgfysfhffgddfg get a chance to the quantity of the SI unit of amount of time to the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity total price for the SI unit of amount of time to the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the quantity of the SI of mathematics which is that branch manager SBI bank of America joined Oct 13th of April so much for your time table and chairs and tables and chairs and tables and chairs and tables and chairs and a picture of the SI unit of the day before and it will not have the same day as well and I will be in broader industry totals for each of you and the SI in the SI in the SI in

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