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If sinx = cos2x, then cos2x(1 + cos2x) is equal to (A) 0 (B) 1 (C) 2 (D) none of these

If sinx = cos2x, then cos2x(1 + cos2x) is equal to
(A) 0 (B) 1
(C) 2 (D) none of these

Grade:10

2 Answers

Karthikk Kumaresan
46 Points
4 years ago
Anoushka Arora,
Answer is (B) 1
Explanation
 
Squaring on both sides, we get
sin2x= cos4x
1-cos2x=cos4x
So cos2x+cos4x = 1
cos2x(1+cos2x) = 1
 
Hence Proved.
 
Warm Regards,
Karthikk Kumaresan
Dhwani
13 Points
2 years ago
RHS
= 1
=cos^2x+ sin^2x
=sinx+sin^2x.           (Given that cos^2x=sinx)
 
=sinx(1+sinx)
=cos^2x(1+cos^2x) =LHS
 
Hence proved.

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