If sin.cosec²+sec= Cot+tan
Answers
Answer:
Step-by-step explanation:
Answer
Given, sinθ=
4
3
We know that,
sinθ=
Hypotenuse
oppositeSide
(Hypotenuse)
2
=(oppositeSide)
2
+(adjacentSide)
2
4
2
=3
2
+(adjacentSide)
2
(adjacentSide)
2
=16−9=7
(adjacentSide)=
7
tanθ=
adjacent side
opposite Side
=
7
3
To prove that
sec
2
θ−1
cosec
2
θ−cot
2
θ
=
3
7
Squaring on both sides,
(
sec
2
θ−1
cosec
2
θ−cot
2
θ
)
2
=(
3
7
)
2
sec
2
θ−1
cosec
2
θ−cot
2
θ
=
9
7
We have,
1+cot
2
θ=csc
2
θ
1+tan
2
θ=sec
2
θ
tan
2
θ
1
=
9
7
(
7
3
)
2
1
=
9
7
9
7
=
9
7
Taking square root on both sides,
3
7
=
3
7
∴
sec
2
θ−1
cosec
2
θ−cot
2
θ
=
3
7