Question

simplify (sin theta + cos theta)²+
(sin theta - cos theta) 2 ?​

Answer 1

Answer:

2

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

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Answer 2

QUESTION:

(sinθ + cosθ)² + (sinθ - cosθ)²

FORMULAS USED:

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

sin²θ + cos²θ = 1

ANSWER:

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

= (1 + 2sinθcosθ) + (1 - 2sinθcosθ)

= 1 + 2sinθcosθ + 1 - 2sinθcosθ

= 2

CONCEPT’s USED:

→» trigonometric identities

→» trigonometric ratios of allied angles