Question

If tan 0 + sin 0 = m and tan0-sin 0 = n, show that : m^2 - n^2 = 4√m√n​

Answer 1

Tanθ+sinθ=m

tanθ-sinθ=n

∴ m+n=tanθ+sinθ+tanθ-sinθ=2tanθ

m-n=tanθ+sinθ-tanθ+sinθ=2sinθ

mn=(tanθ+sinθ)(tanθ-sinθ)

     =tan²θ-sin²θ

∴, m²-n²

=> (m+n)(m-n)

=> 2tanθ.2sinθ

=> 4sinθtanθ

4√mn

=> 4√(tan²θ-sin²θ)

=> 4√(sin²θ/cos²θ-sin²θ)

=> 4√sin²θ(1/cos²θ-1)

=> 4sinθ√(1-cos²θ)/cos²θ

=> 4sinθ/cosθ√sin²θ [∵, sin²θ+cos²θ=1]

=> 4sinθtanθ

∴ LHS=RHS (proved)

Answer 2

Step-by-step explanation:

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