sec theta minus cosec theta into 1 + tan theta + cot theta is equal to tan theta into sec theta minus cos theta into cosec theta
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Step-by-step explanation:
(1+tanθ+secθ)(1+cotθ−cscθ)
=(1+
cosθ
sinθ
+
cosθ
1
)(1+
sinθ
cosθ
−
sinθ
1
)
=
cosθ.sinθ
(cosθ+sinθ+1)(sinθ+cosθ−1)
=
cosθsinθ
(cosθ+sinθ)
2
−1
=
cosθsinθ
cos
2
θ+sin
2
θ+2cosθsinθ−1
=
cosθsinθ
1−1+2sinθcosθ
=2
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