sinθ(1+tanθ)+cosθ(1+cotθ)=secθ +cosecθ
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Answer:
L:H:S = sinθ(1+tanθ)+cosθ(1+cotθ)
=sinθ(1+
cosθ
sinθ
)+cosθ(1+
sinθ
cosθ
)
=sinθ
cosθ
(sinθ+cosθ)
+cosθ
sinθ
(sinθ+cosθ)
=(sinθ+cosθ)(
cosθ
sinθ
+
sinθ
cosθ
)
=
sinθcosθ
(sinθ+cosθ)
(sin
2
θ+cos
2
θ)
=(
cosθ
1
+
sinθ
1
)
=secθ+cosecθ=R:H:S (proved)
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