(Q18)Given cot θ=
7
8
then evaluate
(i)
(1+sinθ)(1-sinθ)
(1+cosθ)(1-cosθ)
Solution:
(1+sinθ)(1-sinθ)
(1+cosθ)(1-cosθ)
=
(1-sin
2
θ)
(1-cos
2
θ)
=
2
θ
2
θ
=
2
θ
2
θ=
(ii)
1+sinθ
cosθ
Solution:
1+sinθ
cosθ
=
1
cosθ
+
sinθ
cosθ
=secθ+tanθ
so cotθ=
7
8
tanθ=
8
7
tan
2
θ=
64
49
From sec
2
θ-tan
2
θ=1
1+tan
2
θ=sec
2
θ---------(1)
1+tan
2
θ=1+
64
49
1+tan
2
θ=sec
2
θ=
(from(1))
secθ=
√
secθ+tanθ=
√
+
clear