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If sinθ + cosθ = √7/2, then what is sinθ – cosθ equal to?
  • a)
    0
  • b)
    1/2
  • c)
    1
  • d)
    √2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If sinθ + cosθ = √7/2, then what is sinθ &ndas...
sinθ + cosθ = √7/2
Squaring both sides;
⇒ sin2θ + cos2θ + 2sinθ.cosθ = 7/4
⇒ 1 + 2sinθ.cosθ = 7/4
⇒ sinθ.cosθ = 3/8
We can write;
sin2θ + cos2θ = (sinθ – cosθ)2 + 2sinθ.cosθ
⇒ (sinθ – cosθ)2 = 1 – 3/4 = 1/4
⇒ (sinθ – cosθ) = 1/2
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If sinθ + cosθ = √7/2, then what is sinθ – cosθ equal to?a)0b)1/2c)1d)√2Correct answer is option 'B'. Can you explain this answer?
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