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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

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

Grade:

4 Answers

Vishal Kamalakannan
30 Points
12 years ago

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
20 Points
9 years ago
tanx tan2x=1tan2x=1/tan
mahdi
20 Points
9 years ago
tanx tan2x=1
tan2x=1/tanx
tan2x=cotx
tan2x=tan(π/2-x)
2x=kπ+π/2-x
x=kπ/3+π/6
Soumyadip
13 Points
one year ago
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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