Question

Prove that. sin4theta-cos4theta=sin2theta-cos2theta

Answer 1

Answer:

Proved below

Step-by-step explanation:

LHS

= sin4theta - cos4theta

= (sin2theta+cos2theta)(sin2theta-cos2theta)         because a2-b2 = (a+b)(a-b)

= 1 * (sin2theta-cos2theta)                                 because sin2theta+cos2theta =1

= sin2theta-cos2theta = RHS

Hence proved

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Answer 2

Answer:

Proved below

Step-by-step explanation:

LHS

= sin4theta - cos4theta

= (sin2theta+cos2theta)(sin2theta-cos2theta)         because a2-b2 = (a+b)(a-b)

= 1 * (sin2theta-cos2theta)                                 because sin2theta+cos2theta =1

= sin2theta-cos2theta = RHS

Hence proved