Prove that : tanθ – cotθ/sinθ cosθ = tan^2θ- cot^2θ
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Step-by-step explanation:
ANSWER
L.H.Q.=
(sinθ⋅cosθ)
tanθ−cotθ
=
(sinθ⋅cosθ)
(
cosθ
sinθ
)−(
sinθ
cosθ
)
=
(sinθ⋅cosθ)
(
(sinθ⋅cosθ)
sin
2
θ−cos
2
θ
)
=
(sin
2
θ⋅cos
2
θ)
sin
2
θ−cos
2
θ
=
sin
2
⋅cos
2
θ
sin
2
θ
−
sin
2
θ⋅cos
2
θ
cos
2
θ
=
cos
2
θ
1
−
sin
2
θ
1
=sec
2
θ−cosec
2
θ
=(1+tan
2
θ)−(1+cot
2
θ)
=1+tan
2
θ−1−cot
2
θ
=tan
2
θ−cot
2
θ=RHQ.
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