Question

if tan theta+sin theta=m and tan theta-sin theta=n show that (m²-n²)=4√mn​​

Answer 1

Answer:

tanθ+sinθ=m and tanθ−sinθ=n

m

2

−n

2

=(m+n)(m−n)

=(tanθ+sinθ+tanθ−sinθ)(tanθ+sinθ−tanθ+sinθ)

=(2tanθ)(2sinθ)

=4tanθsinθ

4

mn

=4

(tanθ+sinθ)(tanθ−sinθ)

4=

((tanθ)

2

−(sinθ)

2

)

=4

(sinθ)

2

(

cos

2

θ

1

−1)

=4sinθ

(cosθ)

2

(1−cos

2

θ)

=4sinθ

(tanθ)

2

=4sinθtanθ

Hence

LHS=RHS (Proved)

Answer 2

Answer:

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