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  1. If sec x + cos x = 2, then the value of sec16 x + cos16 x will be
    1. √3
    2. 2
    3. 1
    4. 0
Correct Option: B

sec x + cos x = 2

⇒
1
+ cosx = 2
cos x

⇒
1 + cos²x
= 2
cos x

⇒ cos²x + 1 = 2 cosx
⇒ cos²x – 2 cosx + 1 = 0
⇒ (cosx – 1)² = 0
⇒ cos –1 = 0
⇒ cos = 1
∴ secx = 1
∴ sec16x + cos16x = 1 + 1 = 2


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