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cos2⁡u+cos2⁡(u+x)−2cos⁡ucos⁡xcos⁡(u+x)=1/2 if

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a

x=π/4

b

u=π/4

c

x=π/2

d

u=π/2

answer is A.

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Detailed Solution

L.H.S =cos2⁡u+cos2⁡(u+x)−[cos⁡(u+x)+cos⁡(u−x)]cos⁡(u+x)=cos2⁡u−cos⁡(u−x)cos⁡(u+x)=cos2⁡u−cos2⁡u−sin2⁡x=sin2⁡xso sin2⁡x=1/2⇒sin⁡x=1/2

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cos2⁡u+cos2⁡(u+x)−2cos⁡ucos⁡xcos⁡(u+x)=1/2 if