Question

If tan???? =1/√7, show that cosec²????-sec²????/cosec²????+sec²????=3/4

Answer 1

Step-by-step explanation:

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Answer 2

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. 

Hope it helps