Question

if sinx + cosx =2 show that sinx^n + cosx^n =2​

Answer 1

sinx + cosx= 2

if we square both sides then

sin^2 x +cos^2 x +2sinxcosx = 4………(sin2x =2sinxcosx)

1 +sin2x =4

sin2x = 3 …….which is not possible so the question may be incorrect

the question can be like ;

sinx + cosy = 2 and we would have to find out sin^n x+cos^ny

in above problem it is possible only when sinx and cosx would have their maximum values so sinx= 1 and cosx=1

hence sin^n x +cos^n x= 1+1 =2