Sin theta cos theta 2 sin theta cos theta 2
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Simplify (sin theta + cos theta)²+(sin theta - cos theta) 2 ?
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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
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