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If cosecθ – sinθ = l and sec θ– cosθ = m, then l2m2(l2 + m2 + 3) = ________ .
- a)1
- b)2
- c)2sinθ
- d)sinθcosθ
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If cosecθ – sinθ = l and sec θ– cos&thet...
We have, l2m2 (l2 + m2 + 3)
= (cosecθ – sinθ)2 (secθ – cosθ)2 {(cosecθ – sinθ)2 + (secθ – cosθ)2 + 3}
= cos6θ + sin6θ + 3 cos2θsin2θ
= {(cos2θ)3 + (sin2θ)3 + 3 cos2θsin2θ
= {(cos2θ + sin2θ)3 – 3 cos2θ sin2θ (cos2θ + sin2θ)} + 3 sin2θcos2θ
= {1 – 3 cos2 sin2θ} + 3 cos2θ sin2θ = 1
= (cosecθ – sinθ)2 (secθ – cosθ)2 {(cosecθ – sinθ)2 + (secθ – cosθ)2 + 3}
= cos6θ + sin6θ + 3 cos2θsin2θ
= {(cos2θ)3 + (sin2θ)3 + 3 cos2θsin2θ
= {(cos2θ + sin2θ)3 – 3 cos2θ sin2θ (cos2θ + sin2θ)} + 3 sin2θcos2θ
= {1 – 3 cos2 sin2θ} + 3 cos2θ sin2θ = 1
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If cosecθ – sinθ = l and sec θ– cos&thet...
The cosecant function (cosec) is the reciprocal of the sine function. It is defined as:
cosec(x) = 1/sin(x)
For example, if sin(x) = 1/2, then cosec(x) = 2.
cosec(x) = 1/sin(x)
For example, if sin(x) = 1/2, then cosec(x) = 2.
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If cosecθ – sinθ = l and sec θ– cosθ = m, then l2m2(l2 + m2 + 3) = ________ .a)1b)2c)2sinθd)sinθcosθCorrect answer is option 'A'. Can you explain this answer?
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