Simplify
cosθ |
1 - tanθ |
sinθ |
1 - cotθ |
Answer:
sinθ + cosθ
- We have been asked to simplify the
+cosθ 1 - tanθ
.sinθ 1 - cotθ - Now,
+cosθ 1 - tanθ sinθ 1 - cotθ
=
+cosθ 1 - sinθ cosθ sinθ 1 - cosθ sinθ
=
+cos2θ cosθ - sinθ sin2θ sinθ - cosθ
=
-sin2θ sinθ - cosθ cos2θ sinθ - cosθ
=sin2θ - cos2θ sinθ - cosθ
=(sinθ - cosθ)(sinθ + cosθ) sinθ - cosθ
= sinθ + cosθ - Therefore,
+cosθ 1 - tanθ
is equal to the sinθ + cosθ.sinθ 1 - cotθ