sinx1sinx2-cosx1cosx2+1=0 the value of tanx1/2*tanx2/2 is alwya equal to?

 

Asked by aahnik.mohanty | 29th May, 2019, 08:00: PM

Expert Answer:

G i v e n colon space sin x subscript 1 space sin x subscript 2 minus cos x subscript 1 space cos x subscript 2 plus 1 equals 0
rightwards double arrow negative cos open parentheses x subscript 1 plus x subscript 2 close parentheses plus 1 equals 0
rightwards double arrow cos open parentheses x subscript 1 plus x subscript 2 close parentheses equals 1
rightwards double arrow fraction numerator 1 minus tan squared open parentheses begin display style fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction end style close parentheses over denominator 1 plus tan squared open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction close parentheses end fraction equals 1
rightwards double arrow 1 minus tan squared open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction close parentheses equals 1 plus tan squared open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction close parentheses
rightwards double arrow tan squared open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction close parentheses equals 0
rightwards double arrow tan open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction close parentheses equals 0
S i n c e space w e space k n o w space t h a t space tan open parentheses x plus y close parentheses equals fraction numerator tan x plus tan y over denominator 1 minus tan x space tan y end fraction
rightwards double arrow tan open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction close parentheses equals fraction numerator tan begin display style x subscript 1 over 2 end style plus tan x subscript 1 over 2 over denominator 1 minus tan x subscript 1 over 2 space tan x subscript 1 over 2 end fraction
rightwards double arrow tan x subscript 1 over 2 space tan x subscript 1 over 2 equals 1 minus fraction numerator tan x subscript 1 over 2 plus tan x subscript 1 over 2 over denominator tan open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction close parentheses end fraction space rightwards arrow space u n d e f i n e d space a s space tan open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction close parentheses equals 0
A l s o comma space tan x subscript 1 over 2 plus tan x subscript 1 over 2 equals tan open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction close parentheses open parentheses 1 minus tan x subscript 1 over 2 space tan x subscript 1 over 2 close parentheses equals 0

Answered by Renu Varma | 30th May, 2019, 10:46: AM