Maximum value of f ( x ) = cos &#x2061;<!-- ⁡ --> x ( sin

Kyla Ayers

Kyla Ayers

Answered question

2022-06-16

Maximum value of f ( x ) = cos x ( sin x + sin 2 x + sin 2 a )

Answer & Explanation

Schetterai

Schetterai

Beginner2022-06-17Added 25 answers

HINT:
y = cos x ( sin x + sin 2 x + sin 2 A )
y sec x sin x = sin 2 x + sin 2 A
Squaring we get
y 2 tan 2 x 2 y tan x + y 2 sin 2 A = 0
As tanx is real, the discriminant
( 2 y ) 2 4 y 2 ( y 2 sin 2 A ) 0
Erin Lozano

Erin Lozano

Beginner2022-06-18Added 7 answers

Let
y = cos x [ sin x + sin 2 x + sin 2 a ] = sin x cos x + cos x sin 2 x + sin 2 a
Now Using CauchySchwartzInequality
We get
( sin 2 x + cos 2 x ) [ cos 2 x + sin 2 x + sin 2 a ] ( sin x cos x + cos x sin 2 x + sin 2 a ) 2
So we get
y 2 ( 1 + sin 2 a ) | y | 1 + sin 2 a

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