If cos alpha + sec alpha = 2, then cos^8 alpha + sec^8 alpha = ....
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1
Answer:
let us assume theta symbol $
given,
cos$+sec$=2,
cos$+1/cos$=2,
cos^$+1=2cos$,
cos^$=2cos$-1
now,
cos^8+sin^8
=> 2cos8–1+1-cos^8
=> 2cos8–1+1–(2cos8–1) [since,cos^$=2cos$-1]
=> 2cos8–1+1–2cos^8+1
=> 1
THEREFORE,cos^8+sin^8=1
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