prove that Cosec theta + cot theta = 1/cosec theta - cot theta
Answers
Answered by
1
Answer:
LHS=
cotA+cosA
cotA−cosA
=
sinA
cosA
+cosA
sinA
cosA
−cosA
=
cosA
cosA
×
cosecA+1
cosecA−1
=
cosecA+1
cosecA−1
=RHS
Answered by
2
Answer:
Answer
cosecθ+cotθ=
cosecθ−cotθ
1
solving LHS.
cosecθ+cotθ = (on rationalizing)
(cosecθ−cotθ)
(cosecθ+cotθ)(cosecθ−cotθ)
cosecθ−cotθ
cosec
2
θ−cot
2
θ
=
sin
2
θ
1
−
sin
2
θ
cos
2
θ
[∵cosecθ=
sinθ
1
cotθ=
sinθ
cosecθ
]
cosecθ−cotθ
sin
2
θ
1−cos
2
θ
=
cosecθ−cotθ
1
[∵1−cos
2
θ=sin
2
θ]
$$\because L.H.S =\frac{1}{cosec\theta-cot\theta} = RHS.
Step-by-step explanation:
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