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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