Question

If cos 0 + sin’O = m then​

Answer 1

tanθ+sinθ=m&tanθ−sinθ=n

⇒mn=(tanθ+sinθ)(tanθ−sinθ)

=tan

2

θ−sin

2

θ

=sin

2

θ(sec

2

θ−1)

=sin

2

θ×tan

2

θ

⇒m

2

−n

2

=(m+n)(m−n)

=(tanθ+sinθ+tanθ−sinθ)(tanθ+sinθ−tanθ+sinθ)

=4tanθsinθ

=4

mn

Hence, proved.