Question

If sina cosa=12/25, theta greater than 0 but less tgan 90. Then sum of all possible values of tana will be??

Answer 1

We know that:  sin a cos a = 12/25

cos a = 12/25 / sin a

cos a = 12 / 25 sin a

sin² a + cos² a = 1

We have to substitute cos a in this formula:

sin² a + ( 12/ 25 sin a )² = 1

sin² a + 144 / 625 sin² a = 1              ( substitution sin² a = t )

It becomes:  t + 144/625 t = 1  / · 625 t  ( multiply both sides by 625 t )

625 t² + 144 = 625 t

625 t² - 625 t + 144 = 0 ( this is quadratic equation )

Solving quadratic equation: t 1/2 = (625 +/- sqrt(390625 - 360000)) / 1250

t 1 = 0.64, t2 = 0.36  or : sin a = 0.8 = 4/5 and sin a = 0.6 = 3/5.

Solutions for sin a and cos a = ( 4/5, 3/5 ) or ( 3/5, 4/5 ).

Finally: tan a = sin a / cos a ;  tan a = 4/3 or tana = 3/4

4/3 + 3/4  = 16/12 + 9/12 = 25/12

Answer: The sum of all tan a is 25/12.