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  • If sinA + sinpower 2 A = 1, then the value of the expression (cospower 2A+ cos poer 4A) is (A) 1(B) 1 by 2(C) 2 (D) 3

If sinA + sin2A = 1, then the value of the expression (cos2A+ cos4A) is

(A) 1                (B)1/2                (C) 2                (D) 3

Answers (1)

Answer.     [A]      

Solution.   It is given that sinA + sin2A = 1          …(*)
sinA = 1 – sin2A
sinA = cos2A               …(1)       ( \because 1 – sin2A = cos2A)
Squaring both sides we get
sin2 A = cos4A             …(2)
Hence cos2A + cos4A =
= sinA + sin2A            {using (1) and (2)}
= sinA + sin2A = 1      (given)
Hence option (A) is correct.

 

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infoexpert27

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