Question

Prove that : sin⁴θ - Cos⁴θ = 1-2cos²θ​

Answer 1

Answer:

here your solution is as follows

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Step-by-step explanation:

so now consider lhs=sin4theta-cos4theta

thus rhs=1-2cos square theta

so now considering lhs

=sin raise to 4 theta-cos raise to 4 theta

=(sin square theta)2-(cos square theta)2

now here (sin square theta)2-(cos square theta)2

is in form a square-b square

so a square-b square=(a+b)(a-b)

thus accordingly

(sin square+cos square theta)(sin square-cos square theta)

=1(sin square-cos square)

because sin square+cos square theta=1

thus sin square-cos square

=1-cos square theta-cos square theta

because 1-cos square theta=sin square theta

thus ie 1-2cos square theta

hence lhs=rhs

thus proved