Tan75/2 ka solution dena sir lekin vistar se
Is that Hindi?
Fortunately mathematics is a universal language.
from tan 2A = 2tanA/(1 - tan^2 A)
tan 75 = 2tan (75/2) /(1 - tan^2 (75/2) )
we know tan 75 = sin 75/cos 75
= sin(45+30)/cos(45+30)
= sin45cos30 + cos45sin30)/(cos45cos30 - sin45sin30)
= ( (√2/2)(√3/2) + (√2/2)(1/2))/( (√2/2)(√3/2) - (√2/2)(1/2) )
= (√6/4 + √2/4)/(√6/4 - √2/4)
= (√6 + √2)/(√6 - √2)
let x = tan 75/2°
then (√6 + √2)/(√6 - √2) = 2x/(1 - x^2)
2x(√6-√2) = √6 + √2 - (√6 + √2) x^2
(√6+√2) x^2 + 2(√6-√2) x - (√6+√2) = 0
x = ( -2(√6-√2) ± √(4(√6-√2)^2 + 4(√6+√2)(√6+√2) )/(2(√6-√2) )
= (-2(√6-√2) ± 8) / (2(√6+√2))
= ( -√6 + √2 ± 8)/(√6 + √2)
but since 75/2 is in the first quadrant, the answer must be positive, so
tan (75/2)° = (-√6 + √2 + 8)/(√6 + √2)
argghhhh!!!!
I made an error somewhere, I should have written it out in full first. Perhaps you can see where I went wrong.
I know my formula is correct and tan 75 is correct as (√6 + √2)/(√6 - √2)
Using (√6+√2) x^2 + 2(√6-√2) x - (√6+√2) = 0
I used Wolfram to solve and it gave me the correct answer of 0.76733
so my error must be in the use of the quadratic formula.
http://www.wolframalpha.com/input/?i=solve+(%E2%88%9A6%2B%E2%88%9A2)+x%5E2+%2B+2(%E2%88%9A6-%E2%88%9A2)+x+-+(%E2%88%9A6%2B%E2%88%9A2)+%3D+0
Tan75/2 ka solution prapt karne ke liye, hum trigonometry ke concept ka upyog karenge. Tan(x) ke tanharkereliye, hum sin(x) par sin(x) aur cos(x) par cos(x) ka parivartan karenge.
Toh, sabse pehle hume 75/2 ko degrees mein convert karna hoga. Kyunki tan(x) ka input degrees mein diya jata hai. degrees= (π/180) * angle(in degrees)
75/2 degrees= (π/180) * (75/2)
Ab, hum is angle ko radians mein convert karenge.
75/2 radians= (π/180) * (75/2)
Ab hum input ko lekar tan(x) ki value nikal sakte hain.
Tan(75/2 radians)= sin(75/2 radians) / cos(75/2 radians)
Tanx ka mujhe pura solution iss angle ke liye nahi milega, lekin yadi aap chahte hain toh aap calculator ya trigonometric tables ka upyog kar sakte hain tan(75/2 radians) ki value ke liye.