If tan theta + sin theta = m and tan theta – sin theta = n show that m^ 2 – n^ 2 = 4 root mn
Answers
Answered by
3
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
Hope helps.......
☺️☺️☺️☺️☺️☺️☺️☺️☺️☺️☺️☺️
Similar questions