` sin x = 3/5 ,x ` तृतीय चतुर्थाश में स्थित है ।

Explanation

ज्ञात है कि ` sin x = 3/5` तथा x दूसरे चतुर्थाश में स्थित है ।
` sin x = 3/5`
` :' " "cosec" x = 1/(sin x) = 1/(3//5) = 1 xx 5/3 = 5/3`
` :. " "cosec" " x = 5/3`
` ( :' x `दूसरे चतुर्थाश में है , अतः sin अनुपात धनात्मक होंगे और शेष अनुपात tan, cot cos और sec ऋणात्मक होंगे ।)
` :' sin^(2) x + cos^(2) x = 1 rArr (3/5)^(2) + cos^(2) x = 1`
` rArr 9/25 + cos^(2) x =1`
` rArr cos^(2) x = 1 - 9/25 rArr cos^(2) = 16/25`
` rArr cos x = pm 4/5`
परन्तु x द्वितीय चतुर्थाश में है ।
अतः ` cos x = -4/5`
` :' sec x = 1/(cos x) rArr sec x = 1/(-4 //5) = 1 xx ((-5)/4) = (-5)/4`
` tan x = (sinx) /(cosx) = (3//5)/(-4//5) = 3/5 xx ((-5)/4) =-3/4`
` :' cot x = (cos x)/(sinx)`
` :. cot x = (-4//5)/(3//5) = -4/5 = 5/3 = -4/3`
अतः ` ""cosec" " x = 5/3, cos x = -4/5`
` sec x = -5/4 , tan = -3/4`
और ` cot x = -4/3`