Answer:
c
Step-by-step explanation:
Ratio in which 180 should be divided is 4:5:9
firstly we need to find the total number of portions
this we can find by adding all the numbers making up the ratio
4 + 5 + 9 = 18
180 is made of 18 portions
size of 1 portion = 180 / 18 = 10
when dividing 180 into the respective ratio 4:5:9 the portions are as follows
4 x 10 = 40
5 x 10 = 50
9 x 10 = 90
therefore when we divide 180 in the ratio 4:5:9
the answer we get is
40 :50: 90
Answer:
See proof below
Step-by-step explanation
cot^2(x) - csc^2(x) = -1
In trigonometry identity
cot^2x = cos²x/sin²x
Csc²x = 1/sin²x
Substitute into the original expression
cos²x/sin²x - 1/sin²x
Find the LCM
(Cos²x-1)/sin²x .... *
Recall that sin²x+cos²x = 1
Sin²x = 1-cos²x
-sin²x = -1+cos²x
-sin²x = cos²x-1 .... **
Substitute ** into *
(Cos²x-1)/sin²x
-sin²x/sin²x
= -1 (RHS)
Therefore cot^2(x) - csc^2(x) = -1 (Proved!)
