prove that sin theta - cos theta = sin theta tan theta
please answer
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Answer:
L.H.S
=
sinθ+cosθ−1
sinθ−cosθ+1
=
tanθ−secθ+1
tanθ+secθ−1
=
tanθ−secθ+1
(tanθ+secθ)−(sec
2
θ−tan
2
θ)
=
tanθ−secθ+1
(tanθ+secθ)−(secθ−tanθ)(secθ+tanθ)
=
(1−secθ+tanθ)
(tanθ+secθ)(1−secθ+tanθ)
=secθ+tanθ
Congugate multiplying by secθ−tanθ
=
secθ−tanθ
sec
2
θ−tan
2
θ
=
secθ−tanθ
1
Explanation:
L.H.S
=
sinθ+cosθ−1
sinθ−cosθ+1
=
tanθ−secθ+1
tanθ+secθ−1
=
tanθ−secθ+1
(tanθ+secθ)−(sec
2
θ−tan
2
θ)
=
tanθ−secθ+1
(tanθ+secθ)−(secθ−tanθ)(secθ+tanθ)
=
(1−secθ+tanθ)
(tanθ+secθ)(1−secθ+tanθ)
=secθ+tanθ
Congugate multiplying by secθ−tanθ
=
secθ−tanθ
sec
2
θ−tan
2
θ
=
secθ−tanθ
1
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