Question

sin theta+cos theta=7/5
and sin theta×cos theta=12/25
find sin theta and cos theta​

Answer 1

Step-by-step explanation:

given sin theta+cos theta=7/5->EQ1

sin theta×cos theta=12/25->EQ2

to find sin theta and cos theta

LET cos theta=7/5-sin theta->EQ3

and EQ3 IN EQ2

THERFORE sin theta(7/5-sin theta)=12/25

-sin^2 theta+7/5sin theta-12/15=0

we can written as

sin^2 theta-7/5sin theta+12/15=0

it is in the form of ax^2+bx+c=0

so using formula (-b+-root of (b^2-4ac))/2a

here a=1,b= -7/5,c=12/25

substituting in formula

(-(-7/5)+-root of (-7/5^2-4(1)(12/25)))/2(1)

(7/5+-root of (49/25-48/100))/2

( 7/5+-root of (1.48))/2

7/5+-1.216/2->7/5+1.216/2(or)7/5-1.216/2

1.3082762531 (or)0.092

let substitute eq 1 first value

1.3082762531 +cos theta=7/5

cos theta=0.092

approximately cos theta =0.092

sin theta =1.3082762531

thank you very much

the problem

it not matching with eq 2