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If tan7theta * tan3theta = 1 , then find the value of theta.

If tan7theta * tan3theta = 1 , then find the value of theta.

Grade:10

1 Answers

Aditya Gupta
2081 Points
5 years ago
hello tithi
we know that tan(x+y)= (tanx+tany)/(1-tanxtany)
let x= 7theta and y=3theta
then tan(x+y)= tan10theta=  (tan7theta+tan3theta)/(1-tan7thetatan3theta)
but 1-tan7thetatan3theta=0 (given)
so tan10theta= infinity
but that is possible only when 10 theta is an odd multiple of 90 degrees
so principle value of theta is 10theta=90
or theta=9 degrees.

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