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ptan theta=q then prove that psin theta +qcos theta/pcos theta+qsin theta=2pq/p²+q²

ptan theta=q then prove that psin theta +qcos theta/pcos theta+qsin theta=2pq/p²+q²

Grade:10

1 Answers

Arun
25763 Points
3 years ago
Let theta = A ; because there is some difficulty to write
theta.
Then
p tanA = q
Hence tan A = q/p
Now take LHS
= (p sinA + q cos A)/(p cosA + q sinA)
divide by cos A in numerator and denominator. And then 
cos A is cancelled by each other.
= (p tanA + q)/(p + q tanA)
Put the values of tanA
= [p*(q/p) + q] / [p + q*(q/p)]
= 2pq/(p2 +q2)
Hence proved

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