cosec theta - cot theta/cosec theta + cot theta=1/2 then sin theta
Answers
Answer:
cosec θ = 1/sin θ
cot θ = 1/tan θ = 1/(sin θ /cos θ ) = cos θ /sin θ
So,
cosec θ - cot θ
= 1/sin θ - cos θ /sin θ
= (1-cos θ )/sin θ
cosec θ - cot θ = (1-cos θ )/sin θ
Again,
Multiplying with sin θ in the numerator and denominator of the RHS,
cosec θ - cot θ
= [sin θ (1 - cos θ)]/sin^2 θ
= [sin θ (1 - cos θ)]/(1 - cos^2 θ)
= [sin θ (1 - cos θ)]/[(1 + cos θ)(1 - cos θ)]
= sin θ /(1 + cos θ)
Hence,
cosec θ - cot θ = (1-cos θ )/sin θ = sin θ /(1 + cos θ)
Answer:
Answer
Open in answr app
1+sinθ
1−sinθ
=
(1+sinθ)(1−sinθ)
(1−sinθ)(1−sinθ)
=
1−sin
2
θ
(1−sinθ)
2
=
cos
2
θ
(1−sinθ)
2
=
cosθ
1−sinθ
=
cosθ
1
−
cosθ
sinθ
=secθ−tanθ
Hence, the answer is secθ−tanθ.
Step-by-step explanation:
Answer
Open in answr app
1+sinθ
1−sinθ
=
(1+sinθ)(1−sinθ)
(1−sinθ)(1−sinθ)
=
1−sin
2
θ
(1−sinθ)
2
=
cos
2
θ
(1−sinθ)
2
=
cosθ
1−sinθ
=
cosθ
1
−
cosθ
sinθ
=secθ−tanθ
Hence, the answer is secθ−tanθ.