Question

f(x) = 2sin(π/4+x)cosx
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Answer 1

f(x) = 2sin(π/4 + x)cosx

use formula, 2sinA.cosB = sin(A + B) + sin(A - B)

so, f(x) = sin(π/4 + x + x) + sin(π/4 + x - x)

f(x) = sin(2x + π/4) + sin(π/4)

f(x) = sin(2x + π/4) + 1/√2

we know, period of sinx = 2π

so, period of sin(2x + π/4) = 2π/2 = π

hence, period of function, f(x) = sin(2x + π/4) + 1/√2 is π

therefore, period of 2sin(π/4 + x)cosx is π

Answer 2

Answer:

Apply the trig identity:

sin (a + b) = sin a.cos b + sin b.cos a

sin (  x+  x + π /4 )  = sin ( π 4 ) .  cos  x + cos ( π /4 ) sin  x =

( √ 2/ 2 )  cos x +  ( √ 2/ 2) sin x = ( √ 2/ 2 )  ( sin  x + cos  x )

Step-by-step explanation: