Question

If sinbeta + cosbeta= 5 by 4 then the value of sinbeta.cosbeta= ?

Answer 1

Answer:

9/32

Step-by-step explanation:

sin β + cos β = 5/4

on squaring on both sides,

sin²β + cos²β + 2*sin β *cos β = 25/16

we know that, sin²β + cos²β = 1 (trigonometric identity)

so,

1 +  2*sin β *cos β = 25/16

2*sin β *cos β = 25/16 - 1

2*sin β *cos β = (25-16)/16

2*sin β *cos β = 9/16

sin β *cos β = (9/16)/2

sin β *cos β = (9/16)*1/2

sin β *cos β = 9/32