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find the range of k so that the equation sin^6x+cos^6x=k-1 has a real solution

find the range of k so that the equation sin^6x+cos^6x=k-1 has a real solution

Grade:12

1 Answers

Soumendu Majumdar
159 Points
5 years ago
Dear Student,
sin^6x + cos^6x = 1 - 3 sin^2xcos^2x
Now,
0\leq sin^2x\leq 1
which implies
0\leq sin^2xcos^2x\leq 1
implies   0\leq 3sin^2xcos^2x\leq 3
implies  -1\leq 3sin^2xcos^2x-1\leq 2 = 1 – k
implies -1\leq 1-k\leq 2
implies   -2\leq -k\leq 1
\Rightarrow -1\leq k\leq 2
 
Hope it helps!
with regards
Soumendu
 

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