Question

(cos theta + sin theta)²+(cos theta-sin theta)² is equal to​

Answer 1

Step-by-step explanation:

According to the Q,

>> (sinθ + cosθ)² + (sinθ - cosθ)²

Using Formula (a + b)² = a² + b² + 2ab

and (a - b)² = a² + b² - 2ab:

>> (sin²θ + cos²θ + 2sinθcosθ) + (sin²θ + cos²θ - 2sinθcosθ)

>> sin²θ + cos²θ + 2sinθcosθ + sin²θ + cos²θ - 2sinθcosθ

We know that (sin²θ + cos²θ) = 1 :

>> 1 + 1 + 2sinθcosθ - 2sinθcosθ

>> 1 + 1

>> 2

Answer 2

Answer:

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

= 1+1

=2

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