SOLUTION: Prove the following identity: cos^4theta + 2cos^2theta sin^2theta + sin^4theta = 1

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Question 32482: Prove the following identity:
cos^4theta + 2cos^2theta sin^2theta + sin^4theta = 1
Answer by sarah_adam(201) About Me  (Show Source):
You can put this solution on YOUR website!
Here iam replacing theta with x
so your question becomes cos^4x + 2cos^2x sin^2x + sin^4x which can be also written as:
(cos^2x)^2+2(co^2x)(sin^2x)+ (sin^2x)^2
If you observe carefully the equation is in the form of a^2+2*a*b+b^2
i.e., (a+b)^2
where a = cos^2x and b = Sin^2x
therfore the equation can be simplified into (cos^2x +sin^2x)^2
But we know cos^2x +sin^2x = 1
therfore (cos^2x +sin^2x)^2 = (1)^2 = 1
Hence Proved