Question

If tan0 +sin0 = m and tan & -sin0 =n, then m2 -n² is equal to a) mn b) (m/n) d) None of these c) 4mn​

Answer 1

Answer:

Correct option is ©️4√mn

Step-by-step explanation:

Tanθ+sinθ=m and tanθ-sinθ=n

∴ m²-n²

=(m+n)(m-n)

=(tanθ+sinθ+tanθ-sinθ)(tanθ+sinθ-tanθ+sinθ)

=(2tanθ)(2sinθ)

=4tanθsinθ

4√mn

=4√(tanθ+sinθ)(tanθ-sinθ)

=4√(tan²θ-sin²θ)

=4√{(sin²θ/cos²θ)-sin²θ}

=4√sin²θ{(1/cos²θ)-1}

=4sinθ√{(1-cos²θ)/cos²θ}

=4sinθ√(sin²θ/cos²θ)

=4sinθ√tan²θ

=4sinθtanθ

∴ LHS=RHS (Proved)

So Answer is 4√mn.

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