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If sinθ+cosecθ=2, the value of sin2 θ+cosec2 θ is :
- a)1
- b)4
- c)2
- d)3
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If sinθ+cosecθ=2, the value of sin2 θ+cosec2 θ...
Given:
sinθ + cosecθ = 2
To Find:
sin^2 θ + cosec^2 θ
Solution:
Step 1: Simplify the given equation
sinθ + cosecθ = 2
(sinθ)(cosecθ) + 1 = 2
sinθ(cosecθ) = 1
Step 2: Find sin^2 θ and cosec^2 θ
sin^2 θ = (sinθ)^2 = (1/(cosecθ))^2 = 1/(cosecθ)^2 = 1/(1/sinθ)^2 = sin^2 θ
cosec^2 θ = (cosecθ)^2 = 1/(sinθ)^2 = 1/(1/cosecθ)^2 = cosec^2 θ
Step 3: Find sin^2 θ + cosec^2 θ
sin^2 θ + cosec^2 θ = sin^2 θ + 1/(sinθ)^2 = sin^2 θ + 1/sin^2 θ
Since sin^2 θ = sinθ and 1/sin^2 θ = cosecθ, we substitute these values:
sin^2 θ + cosec^2 θ = sinθ + cosecθ = 2
Therefore, sin^2 θ + cosec^2 θ = 2.
Therefore, the correct answer is option 'C'.
sinθ + cosecθ = 2
To Find:
sin^2 θ + cosec^2 θ
Solution:
Step 1: Simplify the given equation
sinθ + cosecθ = 2
(sinθ)(cosecθ) + 1 = 2
sinθ(cosecθ) = 1
Step 2: Find sin^2 θ and cosec^2 θ
sin^2 θ = (sinθ)^2 = (1/(cosecθ))^2 = 1/(cosecθ)^2 = 1/(1/sinθ)^2 = sin^2 θ
cosec^2 θ = (cosecθ)^2 = 1/(sinθ)^2 = 1/(1/cosecθ)^2 = cosec^2 θ
Step 3: Find sin^2 θ + cosec^2 θ
sin^2 θ + cosec^2 θ = sin^2 θ + 1/(sinθ)^2 = sin^2 θ + 1/sin^2 θ
Since sin^2 θ = sinθ and 1/sin^2 θ = cosecθ, we substitute these values:
sin^2 θ + cosec^2 θ = sinθ + cosecθ = 2
Therefore, sin^2 θ + cosec^2 θ = 2.
Therefore, the correct answer is option 'C'.
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Community Answer
If sinθ+cosecθ=2, the value of sin2 θ+cosec2 θ...
Square the given equation, then
(sin x + cosec x)^2 = 4
sin^2 x + cosec^2 x + 2sin x cosecx =4
sin^2 x + cosec^2 x + 2 = 4
sin^2 x + cosec^2 x = 2
Option C
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If sinθ+cosecθ=2, the value of sin2 θ+cosec2 θ is :a)1b)4c)2d)3Correct answer is option 'C'. Can you explain this answer?
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If sinθ+cosecθ=2, the value of sin2 θ+cosec2 θ is :a)1b)4c)2d)3Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If sinθ+cosecθ=2, the value of sin2 θ+cosec2 θ is :a)1b)4c)2d)3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sinθ+cosecθ=2, the value of sin2 θ+cosec2 θ is :a)1b)4c)2d)3Correct answer is option 'C'. Can you explain this answer?.
If sinθ+cosecθ=2, the value of sin2 θ+cosec2 θ is :a)1b)4c)2d)3Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If sinθ+cosecθ=2, the value of sin2 θ+cosec2 θ is :a)1b)4c)2d)3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sinθ+cosecθ=2, the value of sin2 θ+cosec2 θ is :a)1b)4c)2d)3Correct answer is option 'C'. Can you explain this answer?.
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