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If x = cosecθ − sinθ and y = secθ − cosθ, then the value of x2y2(x2 + y2 + 3)
- a)0
- b)1
- c)2
- d)3
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Ifx = cosecθ − sinθandy = secθ − cos&the...
Given:
If x = cosecθ - sinθ and y = secθ - cosθ
To find:
The value of x^2y^2(x^2 + y^2 + 3)
Solution:
Step 1: Calculate x^2 and y^2
x^2 = (cosecθ - sinθ)^2
x^2 = cosec^2θ + sin^2θ - 2cosecθsinθ
y^2 = (secθ - cosθ)^2
y^2 = sec^2θ + cos^2θ - 2secθcosθ
Step 2: Substitute x^2 and y^2 in the expression
x^2y^2(x^2 + y^2 + 3) = (cosec^2θ + sin^2θ - 2cosecθsinθ)(sec^2θ + cos^2θ - 2secθcosθ)(cosec^2θ + sin^2θ + sec^2θ + cos^2θ + 3)
Step 3: Simplify the expression
Upon simplification, the expression reduces to:
x^2y^2(x^2 + y^2 + 3) = 1
Therefore, the correct answer is option 'B' - 1.
If x = cosecθ - sinθ and y = secθ - cosθ
To find:
The value of x^2y^2(x^2 + y^2 + 3)
Solution:
Step 1: Calculate x^2 and y^2
x^2 = (cosecθ - sinθ)^2
x^2 = cosec^2θ + sin^2θ - 2cosecθsinθ
y^2 = (secθ - cosθ)^2
y^2 = sec^2θ + cos^2θ - 2secθcosθ
Step 2: Substitute x^2 and y^2 in the expression
x^2y^2(x^2 + y^2 + 3) = (cosec^2θ + sin^2θ - 2cosecθsinθ)(sec^2θ + cos^2θ - 2secθcosθ)(cosec^2θ + sin^2θ + sec^2θ + cos^2θ + 3)
Step 3: Simplify the expression
Upon simplification, the expression reduces to:
x^2y^2(x^2 + y^2 + 3) = 1
Therefore, the correct answer is option 'B' - 1.
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Community Answer
Ifx = cosecθ − sinθandy = secθ − cos&the...
Similarly y = sinθcosθ
x2 + y2 + 3 = (sec2θ + cosec2θ)
Now putting above values in given equation, and after solving it will be reduced to 1
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Ifx = cosecθ − sinθandy = secθ − cosθ, then the value of x2y2(x2+ y2+ 3)a)0b)1c)2d)3Correct answer is option 'B'. Can you explain this answer?
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