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Question

If x1,x2,x3,....,xn are in A.P. whose common difference is α, then the value of sin α(secx1 secx2+secx2 secx3 +... ...+secxn1 secxn)=

A
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B
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C
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D
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Solution

The correct option is A
We have sin α sec x1 sec x2+sin α sec x2 sec x3+....
...+sin α sec xn1sec xn
=sin(x2x1)cos x1 cos x2+sin(x3x2)cos x2 cos x3+...+sin(xnxn1)cos xn1 cos xn=tan x2tan x1+tan x3tan x2+...+tan xntan xn1=tan xntan x1=sin(xnx1)cos xn cos x1=sin(n1)αcos xn cos x1
{( xn=x1+(n1)α)}

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