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USPshnik [31]
3 years ago
11

Simplify: (sin Θ − cos Θ)2 + (sin Θ + cos Θ)2 options are 1 2 sin2 Θ cos2 Θ

Mathematics
1 answer:
I am Lyosha [343]3 years ago
6 0

Answer:

2 is the right answer.

Step-by-step explanation:

(sin∅-cos∅)²+(sin∅+cos∅)² in this expression we will open the brackets first by squaring the expressions given inside.

(sin²∅+cos²∅-2sin∅cos∅)+(sin²∅+cos²∅+2sin∅cos∅)

Since (a+b)² = a²+b²+2ab and (a-b)² = a²+b²-2ab

⇒(1-2sin∅cos∅) + (1+2sin∅cos∅)

Since (sin²∅+cos²∅) =1

⇒ 1-2sin∅cos∅+1+2sin∅cos∅

⇒ 1+1

⇒ 2

Therefore the option 2 is right answer.


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source: https://www.jiskha.com/questions/1857280/estimate-how-many-times-larger-1-9x10-8-is-than-4-2x10-13

credit: mathhelper

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