SOLUTION: if tan theta = 1 / root 7, show that (cosec ^2 theta - sec ^2 theta )/cosec^2 theta +sec^2 theta )=3/4

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Question 992757: if tan theta = 1 / root 7, show that (cosec ^2 theta - sec ^2 theta )/cosec^2 theta +sec^2 theta )=3/4
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,
if tan theta = 1 / root 7
cosec theta = root 8/1
sec theta = root 8/root 7
...........
(cosec ^2 theta - sec ^2 theta )/cosec^2 theta +sec^2 theta )
(root 8/1)^2 - (root 8/root 7)^2/ (root 8/1)^2 + (root 8/root 7)^2
(8/1 - 8/7) / (8/1 + 8/7)
((56 -8)/7 / ((56 + 8)/7
[48/7 / 64/7]
[ 48 x 7]/ [7 x 64)
Cancel 7's top and bottom
=48/64
Divide top and bottom by 16
= 3/4
Hope this helps :-)