Question
Download Solution PDFIf sinθ + cosθ = √2, then what is the value of 8 sinθ cosθ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
If sinθ + cosθ = √2
Formula used:
(sinθ + cosθ)2 = sin2θ + cos2θ + 2sinθcosθ
Calculation:
(sinθ + cosθ)2 = (√2)2
⇒ sin2θ + cos2θ + 2sinθcosθ = 2
We know that sin2θ + cos2θ = 1
⇒ 1 + 2sinθcosθ = 2
⇒ 2sinθcosθ = 1
⇒ sinθcosθ = 1/2
⇒ 8sinθcosθ = 8 × 1/2 = 4
∴ The correct answer is option (4).
Last updated on Feb 22, 2025
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