Answers

2015-10-04T14:28:09+05:30
Tan theta = opposite side/adjacent side
tan theta=1/root 7
Therefore,
Opposite side=1 and Adjacent side= root 7
 By Pythogoras theorem
Hypotenuse^2=Adjacent^2+Opposite^2
Hypotenuse^2 = root 7^2 + 1^2
Hypotenuse^2 = 7+1
Hypotenuse = root 8

Sin theta = Opposite/ Hypotenuse
Sin theta = 1/root 8
Therefore,
cosec theta = root 8/1

cos theta = Adjacent/Hypotenuse
Cos theta = root 7/root 8
Therfore,
sec theta = root 8/ root 7

Now,
Cosec^2 theta - Sec^2 theta / Cosec^2 theta + Sec^2 theta

Root 8^2/1^2 - Root8^2/root 7^2 / root 8^2/1^2 + root8^2/root 7^2

8/1-8/7 / 8/1+8/7

56-8/7 /56+8/7

48/7 / 64/7

48/7 *7/64
 
48/64

3/4

The answer is 3/4. 
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