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 If a1, a2....an are in A.P. with common difference d ¹ 0, then the sum of the series
(sin d) [cosec a1 cosec a2 + cosec a2 cosec a3 +..... ......+ cosec an – 1 cosec an]
  • a)
     sec a1 – sec an
  • b)
    cosec a1 – cosec an 
  • c)
    cot a1 – cot an
  • d)
     tan a1 – tan an
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If a1, a2....anare in A.P. with common difference d ¹ 0, then the...
A₁ , A₂ , A₃ , .......An are in AP and common difference is d
so, d = A₂ - A₁ = A₃ - A₂ = A₄ - A₃ =...... =An - An-1 -------(1)
 
Now, sind[cosecA₁.cosecA₂ + cosecA₂.cosecA₃ + cosecA₃.cosecA₄ ...........+ cosecAn-1.cosecAn ]
⇒ sind[1/sinA₁.sinA₂ + 1/sinA₂.sinA₃ + 1/sinA₃.sinA₄ + .........+ 1/sinAn₋₁.sinAn]
⇒ sin d/sinA₁.sinA₂ + sind/sinA₂.sinA₃ + sind/sinA₃.sinA₄ + .......+sind/sinAn₋₁.sinAn
⇒ sin(A₂ - A₁)/sinA₁.sinA₂ + sin(A₃ - A₂)/sinA₂.sinA₃ + sin(A₄ - A₃)/sinA₃.sinA₄ + .......+ sin(An-1 - An)/sinAn-1.sinAn [ from equation (1)
⇒ (sinA₁.cosA₂ - cosA₁.sinA₂)/sinA₁.sinA₂ + (sinA₂.cosA₃ - cosA₂.sinA₃)/sinA₂.sinA₃ +.........+ (sinAn-1.cosAn - cosAn-1.sinAn)/sinAn-1.sinAn
⇒cotA₂ - cotA₁ + cotA₃ - cotA₂ + cotA₄ - cotA₃ + .........cotAn - cotAn-1
⇒cotAn - cotA₁
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Most Upvoted Answer
If a1, a2....anare in A.P. with common difference d ¹ 0, then the...
A₁ , A₂ , A₃ , .......An are in AP and common difference is d
so, d = A₂ - A₁ = A₃ - A₂ = A₄ - A₃ =...... =An - An-1 -------(1)
 
Now, sind[cosecA₁.cosecA₂ + cosecA₂.cosecA₃ + cosecA₃.cosecA₄ ...........+ cosecAn-1.cosecAn ]
⇒ sind[1/sinA₁.sinA₂ + 1/sinA₂.sinA₃ + 1/sinA₃.sinA₄ + .........+ 1/sinAn₋₁.sinAn]
⇒ sin d/sinA₁.sinA₂ + sind/sinA₂.sinA₃ + sind/sinA₃.sinA₄ + .......+sind/sinAn₋₁.sinAn
⇒ sin(A₂ - A₁)/sinA₁.sinA₂ + sin(A₃ - A₂)/sinA₂.sinA₃ + sin(A₄ - A₃)/sinA₃.sinA₄ + .......+ sin(An-1 - An)/sinAn-1.sinAn [ from equation (1)
⇒ (sinA₁.cosA₂ - cosA₁.sinA₂)/sinA₁.sinA₂ + (sinA₂.cosA₃ - cosA₂.sinA₃)/sinA₂.sinA₃ +.........+ (sinAn-1.cosAn - cosAn-1.sinAn)/sinAn-1.sinAn
⇒cotA₂ - cotA₁ + cotA₃ - cotA₂ + cotA₄ - cotA₃ + .........cotAn - cotAn-1
⇒cotAn - cotA₁
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Community Answer
If a1, a2....anare in A.P. with common difference d ¹ 0, then the...
C
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If a1, a2....anare in A.P. with common difference d ¹ 0, then the sum of the series(sin d) [cosec a1cosec a2+ cosec a2cosec a3+..... ......+ cosec an –1cosec an]a)sec a1–sec anb)cosec a1–cosec anc)cot a1–cot and)tan a1–tan anCorrect answer is option 'C'. Can you explain this answer?
Question Description
If a1, a2....anare in A.P. with common difference d ¹ 0, then the sum of the series(sin d) [cosec a1cosec a2+ cosec a2cosec a3+..... ......+ cosec an –1cosec an]a)sec a1–sec anb)cosec a1–cosec anc)cot a1–cot and)tan a1–tan anCorrect 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 a1, a2....anare in A.P. with common difference d ¹ 0, then the sum of the series(sin d) [cosec a1cosec a2+ cosec a2cosec a3+..... ......+ cosec an –1cosec an]a)sec a1–sec anb)cosec a1–cosec anc)cot a1–cot and)tan a1–tan anCorrect 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 a1, a2....anare in A.P. with common difference d ¹ 0, then the sum of the series(sin d) [cosec a1cosec a2+ cosec a2cosec a3+..... ......+ cosec an –1cosec an]a)sec a1–sec anb)cosec a1–cosec anc)cot a1–cot and)tan a1–tan anCorrect answer is option 'C'. Can you explain this answer?.
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