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If Cos x – Sin x = √2 Sin x, find the value of Cos x + Sin x:
- a)√2 Cos x
- b)√2 Cosec x
- c)√2 Sec x
- d)√2 Sin x Cos x
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If Cos x – Sin x = √2 Sin x, find the value of Cos x + Sin...
Cos x – Sin x = √2 Sin x
⇒ Cos x = Sin x + √2 Sin x
⇒ Sin x = (√2 - 1) Cos x
⇒ Sin x = √2 Cos x - Cos x
⇒ Sin x + Cos x = √2 Cos x
⇒ Cos x = Sin x + √2 Sin x
⇒ Sin x = (√2 - 1) Cos x
⇒ Sin x = √2 Cos x - Cos x
⇒ Sin x + Cos x = √2 Cos x
Most Upvoted Answer
If Cos x – Sin x = √2 Sin x, find the value of Cos x + Sin...
Given
cosX - sinX = √2 sinX
so,
cosX = √2sinX + sinx
cosX = sinX(√2+1)
sinX = cosX/(√2 +1)
multiply and divide R.H.S with (√2 - 1)
that gives,
sinX = (cosX/(√2+1)) × (√2-1/√2-1)
sinX = cosX × (√2 - 1)
sinX = √2 cosX - cosX
sinX + cosX = √2 cosX = option A
cosX - sinX = √2 sinX
so,
cosX = √2sinX + sinx
cosX = sinX(√2+1)
sinX = cosX/(√2 +1)
multiply and divide R.H.S with (√2 - 1)
that gives,
sinX = (cosX/(√2+1)) × (√2-1/√2-1)
sinX = cosX × (√2 - 1)
sinX = √2 cosX - cosX
sinX + cosX = √2 cosX = option A
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Community Answer
If Cos x – Sin x = √2 Sin x, find the value of Cos x + Sin...
Multiplying (√2 - 1) to the numerator and denominator will give the result
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If Cos x – Sin x = √2 Sin x, find the value of Cos x + Sin x:a)√2 Cos xb)√2 Cosec xc)√2 Sec xd)√2 Sin x Cos xCorrect answer is option 'A'. Can you explain this answer?
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