Question

15. If tan theta + sin theta = m and tan theta - sin theta =n, then m^2 - n^2 is equal to​

Answer 1

Step-by-step explanation:

Given, m=tanθ+sinθ,n=tanθ−sinθ

We need to show m

2

−n

2

=4

mn

Taking L.H.S.,

m

2

−n

2

=(tanθ+sinθ)

2

−(tanθ−sinθ)

2

=tan

2

θ+sin

2

θ+2tanθ.sinθ−tan

2

θ−sin

2

θ+2tanθ.sinθ

=4tanθ.sinθ

Now, taking R.H.S.,

4

mn

=4

(tanθ+sinθ)(tanθ−sinθ)

=4

tan

2

θ−sin

2

θ

=4

cos

2

θ

sin

2

θ

−sin

2

θ

=4

cos

2

θ

sin

2

θ(1−cos

2

θ)

=4

sin

2

θ.tan

2

θ

=4tanθ.sinθ

Therefore, L.H.S. = R.H.S.

Answer 2

Answer:

given in copy. see it carefully