Question
If x1,x2,x3,......,xn are in A.P. whose common difference is a, then the value of sin α(sec x1 sec x2 + sec x2 sec x3 +....... + sec xn−1, sec xn)=
Answer: Option A
:
A
(a) We havesin α sec x1 sec x2 + sin α sec x2 sec x3 +....... + sin α sec xn−1, sec xn)
=sin(x2−x1)cosx1cosx2 +sin(x3−x2)cosx2cosx3 + ........ +sin(xn−xn−1)cosxn−1cosxn
= tan x2 -tan x1 +tan x3 -tan x2 + .......... +tan xn -tan xn−
=tan xn -tan x1 =sin(xn−xn−1)cosxn−1cosx1 = sin(n−1)αcosxncosx1 {(∵ xn = x1 + (n - 1)α)}
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:
A
(a) We havesin α sec x1 sec x2 + sin α sec x2 sec x3 +....... + sin α sec xn−1, sec xn)
=sin(x2−x1)cosx1cosx2 +sin(x3−x2)cosx2cosx3 + ........ +sin(xn−xn−1)cosxn−1cosxn
= tan x2 -tan x1 +tan x3 -tan x2 + .......... +tan xn -tan xn−
=tan xn -tan x1 =sin(xn−xn−1)cosxn−1cosx1 = sin(n−1)αcosxncosx1 {(∵ xn = x1 + (n - 1)α)}
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