Simplest form of 22+2+2+2cos4x is
secx2
secx
cscx
1
Explanation for the correct option:
Simplifying the given expression:
22+2+2+2cos4x...(i)
Now Solving,
⇒2+2cos4x⇒21+cos2(2x)⇒22cos2(2x)⇒4cos2(2x)
Therefore,
4cos2(2x)=2cos2x
Now,
⇒2+2+2cos4x⇒2+2cosx⇒2(1+cos2x)⇒22cos2x⇒2cosx
And
2+2+2+2cos4x⇒2+2cosx⇒2(1+cosx)⇒22cos2x2=2cosx2...(ii)
From (i) and (ii)
22+2+2+2cos4x⇒22cosx2⇒secx2
Therefore, the correct answer is option (A).
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