Question

15. If tan 0+ sin 0 =m and tan 0 - sin 0 =n, then m^2– n^2 is equal to ​

Answer 1

Answer:

4√mn

Step-by-step explanation:

tanΘ + sinΘ = m

tanΘ - sinΘ = n

=> mn = tan^2Θ - sin^2Θ

          = sin^2Θ/cos^2Θ - sin^2Θ

          = sin^2Θ(1/cos^2Θ - 1)

          = sin^2Θ(sec^2Θ - 1)

          = sin^2Θtan^2Θ

=> √mn = sinΘtanΘ

Now,

m^2 - n^2  = (m + n)(m - n)

= (tanΘ + sinΘ + tanΘ - sinΘ)(tanΘ + sinΘ - tanΘ + sinΘ)

= (2tanΘ)(2sinΘ)

= 4tanΘsinΘ

= 4√mn

Hope it helps :)

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