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Consider the following statements:
1. (sec2 θ - 1) (1 - cosec2 θ) = 1
2. sin θ (1 + cos θ)-1 + (1 + cos θ) (sin θ)-1 = 2 cosec θ
Q. Which of the above is/are correct?
  • a)
    1 only
  • b)
    2 only
  • c)
    Both 1 and 2
  • d)
    Neither 1 nor 2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Consider the following statements:1. (sec2θ - 1) (1 - cosec2&the...
Statement 1:
Sec2 θ - 1 = tan2 θ and cosec2 θ - 1 = cot2 θ
∴ (sec2 θ - 1) (1 - cosec2 θ) = tanθ (-cot2 θ) = -1 [∵ tan θ × cot θ = 1]
∴ Statement 1 is wrong
Statement 2:
sin θ/(1 + cos θ) + (1 + cos θ)/sinθ = [sinθ + (1 + cos θ)2]/[(1 +cos θ) sinθ]
⇒ [sin2 θ + 1 +2cos θ + cosθ]/[(1 +cos θ) sinθ] [∵ (a + b)2 = a2 + 2ab + b2]
⇒ [1 + 1 + 2cos θ]/[(1 + cos θ) sinθ] [∵ sinθ + cosθ = 1]
⇒ [2 + 2cos θ]/[(1 + cos θ) sinθ]
⇒ 2 [1 + cosθ]/[(1 + cos θ) sinθ]
⇒ 2/sinθ = 2 cosecθ [∵ 1/sin θ = cosec θ]
Statement 2 is correct
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Consider the following statements:1. (sec2θ - 1) (1 - cosec2θ) = 12. sin θ (1 + cos θ)-1+ (1 + cos θ) (sin θ)-1= 2 cosec θQ. Which of the above is/are correct?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'B'. Can you explain this answer?
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