Question

prove that (sin+cos)²-(sin-cos)²=2sin2​

Answer 1

Step-by-step explanation:

Given

(sina+cosa)^2-(sina-cosa)^2

(sina+cosa+sina-cosa)(sina+cosa-sina+cosa)

2sina×2cosa

2sin2a

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Answer 2

We have,

LHS = sin

4

A - cos

4

A

⇒ LHS = (sin

2

A)

2

−(cos

2

A)

2

⇒ LHS = (sin

2

A+cos

2

A)(sin

2

A−cos

2

A)

⇒ LHS = sin

2

A −cos

2

A [∵sin

2

A+cos

2

A=1]

⇒ LHS = sin

2

A −(1−sin

2

A ) = 2sin

2

A−1

⇒ LHS = 2(1−cos

2

A)−1=1−2cos

2

A = RHS