if tan x . tan 2x = 1 then the value of
sin^2 (2x)+ tan^2 (2x) is equal to
3/4
10/3
15/4
3
sachin goel , 13 Years ago
Grade
Trigonometry> provide full solution...
4 AnswersVishal Kamalakannan
tanx.tan2x=1
expand tan2x and take denominator to the other side.
u will get tanx =1/1.732 which implies x=30 deg.
so substitute the value in the given expression to get the answer.
mahdi
tanx tan2x=1tan2x=1/tan
mahdi
tanx tan2x=1
tan2x=1/tanx
tan2x=cotx
tan2x=tan(π/2-x)
2x=kπ+π/2-x
x=kπ/3+π/6
Soumyadip
tanxtan2x=1
Or, tanx(2tanx/1-tan²x)=1. [tan2x=2tanx/1-tan²x]
Or,2tan²x/1-tan²x=1
Or, 2tan²x=1-tan²x
Or,3tan²x=1
Or,tan²x=1/3
Or,tanx=1/3
Hence X=30°
Sin²(2x)+tan²(2x)
=Sin²60°+tan²+60°
=(√3/2)²+(√3)²
=3/4+3
=15/4
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