Q. 103.6( 23 Votes )

If tan θ + sin θ

Answer :

Given,


tan θ + sin θ = m …(1)


tan θ – sin θ = n …(2)


As we have to prove: m2 – n2 = 4 sin θ tan θ


if we find out the expression of sin θ and tan θ in terms of m and n, we can get the desired expression to be proved.


Adding equation 1 and 2 to get the value of tan θ.


2 tan θ = m + n …(3)


Similarly, on subtracting equation 2 from 1, we get-


2sin θ = m – n …(4)


Multiplying equation 3 and 4 –


2sin θ (2tan θ) = (m + n)(m – n)


4 sin θ tan θ = m2 – n2


Hence,


m2 – n2 = 4 sin θ tan θ


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