Question

if (sin teta +cos teta )=a and (sin³teta +cos³teta )=b then (3a -2b)=​

Answer 1

Answer:

a³

Step-by-step explanation:

given,

sinA+cosA = a   &

sin³A + cos³A = b

consider a³

= (sinA+cosA)³

= sin³A+cos³A+ 3sinA.cosA(sinA+cosA)

a³ = b + 3sinA.cosA *a       ------------------- (1)

now consider a²

= (sinA+cosA)²

= sin²A+cos²A+2sinAcosA

a² = 1+2sinAcosA

=> 2sinAcosA = a²-1  

=> sinAcosA = (a²-1 )/2

so, (1) => a³ = b + 3 [(a²-1 )/2] *a

         => a³ = b + [(3a³ - 3a)/2]

         => 2a³ = 2b +3a³ - 3a

         =>  3a  - 2b = 3a³ - 2a³

         =>  3a  - 2b = a³