If tan a + sin is equal to m and 10 m minus sin is equal to n show that n square minus n square is equal to 4 root mn
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HELLO DEAR,
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--------(1)
-----------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-----------(1)
from--(1) and----(2)
m²-n² = 4√mn
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