Question

if sin@cos@=12/25 then find the sum of all possible value of tan@ (0<@>90)

Answer 1

Answer:

Tan a = 4/3  & 3/4

Step-by-step explanation:

sinacosa=12/25

squaring both sides

sin²acos²a=144/625

using cos²a = 1 - sin²a

=> sin²a( 1 - sin²a) = 144/625

=> 625 Sin²a - 625(Sin²a)² = 144

=> 625(Sin²a)² - 625 Sin²a + 144 = 0

=> 625(Sin²a)² - 225Sin²a - 400Sin²a + 144= 0

=> 25Sin²a(25Sin²a - 9) - 16(25Sin²a - 9) = 0

=> (25Sin²a - 16)(25Sin²a - 9) = 0

=> Sin²a = 16/25  &  9/25

Cos²a = 9/25    &   16/25

tan²a = Sin²a/Cos²a  =  16/9    &  9/16

=> Tan a = 4/3  & 3/4   ( only + ve values as 0<a<90)