If sinx sin2 x 1 then what is the value of cos8 x 2cos6 x cos4 x ........

Quantitative Aptitude (CDS) Trignometry

If sinx + sin² x = 1, then what is the value of cos⁸x + 2cos⁶ x + cos⁴ x ?

As sin sin x +x=1
sin sin x=1-x
=>sin sin x = x …….. (i)
Now,
x + 2x + x = (x )² + 2x . x+ (x )²
= (x + x)²
=[As, x =sin sin x ]
= (1)² = 1

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