Find sin 2theta if theta is in the first quadrant and tan theta = 40/9 ??

1 Answer
Ratnaker Mehta
Jul 18, 2018

# 720/1681#.

Explanation:

Using the Identity, #sin2theta=(2tantheta)/(1+tan^2theta)#, we get,

#sin2theta=(2*40/9)/{1+(40/9)^2}#,

#=80/9-:1681/81#.

# rArr sin2theta=720/1681#.

#theta in Q_1 rArr 0 lt theta lt pi/2 rArr 0 lt 2theta lt pi#.

#:. sin2theta gt 0#.

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