(Q11)Evaluate the following:
i. (1 + tan θ + sec θ) (1 + cot θ – cosec θ)
Given (1 + tan θ + sec θ) (1 + cot θ – cosec θ)
= (
1
1
+
θ
θ
+
1
θ
)(
1
1
+
θ
θ
-
1
θ
)
= (
(
θ +
θ) + 1
θ
)(
(
θ +
θ) - 1
θ
)
=
(
θ +
θ)
2
- (
)
2
θ.
θ
[∵(a + b)(a - b) = a
2
- b
2
]
=
2
θ +
2
θ + 2 sinθ cosθ - 1
θ.
θ
[∵(a + b)
2
= a
2
+ b
2
+ 2ab]
=
+ 2 sin θ . cos θ - 1
θ .
θ
[∵ cos
2
θ + sin
2
θ = 1]
=
sinθ . cosθ
θ .
θ
=
Clear