Find all (a,b), such that y = cos 2 </msup> &#x2061;<!-- ⁡ --> x +

Gretchen Schwartz

Gretchen Schwartz

Answered question

2022-07-06

Find all (a,b), such that y = cos 2 x + cos 2 ( x + a ) + 2 cos x cos ( x + a ) cos b is constant for all x R

Answer & Explanation

Asdrubali2r

Asdrubali2r

Beginner2022-07-07Added 14 answers

HINT:
S = cos 2 x + cos 2 ( x + a ) + 2 cos x cos ( x + a ) cos b
= 1 + cos 2 ( x + a ) sin 2 x + 2 cos x cos ( x + a ) cos b
Using Prove that cos ( A + B ) cos ( A B ) = cos 2 A sin 2 B
S = 1 + cos a cos ( 2 x + a ) + { cos ( 2 x + a ) + cos a } cos b
= 1 + cos a cos b + ( cos b + cos a ) cos ( 2 x + a )

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