(tan²(<em>θ</em>) cos²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>))
Recall that
tan(<em>θ</em>) = sin(<em>θ</em>) / cos(<em>θ</em>)
so cos²(<em>θ</em>) cancels with the cos²(<em>θ</em>) in the tan²(<em>θ</em>) term:
(sin²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>))
Recall the double angle identity for cosine,
cos(2<em>θ</em>) = 2 cos²(<em>θ</em>) - 1
so the 1 in the denominator also vanishes:
(sin²(<em>θ</em>) - 1) / (2 cos²(<em>θ</em>))
Recall the Pythagorean identity,
cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1
which means
sin²(<em>θ</em>) - 1 = -cos²(<em>θ</em>):
-cos²(<em>θ</em>) / (2 cos²(<em>θ</em>))
Cancel the cos²(<em>θ</em>) terms to end up with
(tan²(<em>θ</em>) cos²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>)) = -1/2
Answer:
354 $ is correct
Step-by-step explanation:
your v id dead
19.......................................
Answer:
A(n) = L(n) × W(n) and 
Step-by-step explanation:
We are given that the length of the rectangular garden is L and width is W.
Also, in terms of 'n',
Length is given by, L(n) = n + 2
Width is given by, W(n) = 0.5n + 1.
Now, we know that, Area of rectangle = Length × Width.
Therefore, area of Kirti's garden is given by, A(n) = L(n) × W(n).
Thus, formula of area in terms of L(n) and W(n) is A(n) = L(n) × W(n).
Moreover, as A(n) = L(n) × W(n).
i.e. A(n) = (n+2) × (0.5n+1)
i.e. 
i.e. 
i.e.
Hence, the formula for area in terms of 'n' is .
