Question

Given y = 2[x] + 3 and y = 3(x – 2] + 5
(I.GIF) then the value of (x + 3y) is 37lamda
where lamda is​

Answer 1

LHS = 2 sin2β + 4 cos (α + β) sin α sin β + cos 2(α + β)

= 2 sin2β + 4 (cos α cos β – sin α sin β) sin α sin β + (cos 2α cos 2β – sin 2α sin 2β)

= 2 sin2β + 4 sin α cos α sin β cos β – 4 sin2α sin2β + cos 2α cos 2β – sin 2α sin 2β

= 2 sin2β + sin 2α sin 2β – 4 sin2α sin2β + cos 2α cos 2β – sin 2α sin 2β

= (1 – cos 2β) – (2 sin2α) (2 sin2β) + cos 2α cos 2β

= (1 – cos 2β) – (1 – cos 2α) (1 – cos 2β) + cos 2α cos 2β

= cos 2α

= RHS

Therefore, 2 sin2β + 4 cos (α + β) sin α sin β + cos 2 (α + β) = cos 2α

Answer 2

Given (x + 3y ) = 37

RHS

y = 2x + 3

LHS

y = 3(x-2) + 5

Since LHS = RHS,

2x + 3 = 3( x-2)

2x + 3 = 3x - 6 +5

3x - 2x = 6+3 - 5

x = 9 -5

= 4

y = 2x + 3

= 2×4 + 3

= 11

x + 3y = 37lamda

4 + ( 3 × 11) = 37 lamda

4 + 33 = 37 lamda

Lamda = 37 / 37

= 1