Question

If x₁, x₂, x₃, ..., xₙ are in A.P. whose common difference is α, then the value of
sinα (sec x₁ sec x₂ + sec x₂ sec x₃ +...+ sec xₙ₋₁ sec xₙ) is
(a) [sin(n-1)α]/[cos x₁ cos xₙ]
(b) [sin nα]/[cos x₁ cos xₙ]
(c) sin(n-1)α cos x₁ cos xₙ
(d) sin nα cos x₁ cos xₙ

Answer 1

Answer:

=> sin@(secx1secx2 + secx2secx3 + .... + secx(n-1)secxn)

=> sin@secx1secx2 + sin@secx2secx3 + ... + sin@secx(n-1)secxn

=> sin(x2-x1)/cosx1cosx2 + sin(x3-x2)/cosx2cosx3 + .... + sin(xn - x(n-1))/cosxncosx(n-1)

=> tanx2 - tanx1 + tanx3 - tanx2 + .... + tanxn - tanx(n-1)

=> tanxn - tanx1

=> sin(xn-x1)/cosxncosx1

=> sin(n-1)@/cosxncosx1

option a

Answer 2

Answer:

Option a is the answer of this question ok