Question

If tan theta =root 7, then sec theta =​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The answer is 3/4

Step-by-step explanation:

Tan theta = opposite side / adjacent side

Tan theta = 1 / root 7

Therefore,

opposite side = 1 and adjacent side = root 7

By pythaogoras theorem

Hypotenuse ^2 = adjacent ^2 + opposite ^2

Hypotenuse ^2 = root 7 ^2 + 1 ^2

Hypotenuse ^2 = 7+1

Hypotenuse ^2 = root 8

Sin theta = opposite / hypotenuse

Sin theta = 1 / root 8

Therefore,

cosec theta = root 8/ 1

cos theta = adjacent / hypotenus

cos theta = root 7 / root 8

Therefore,

sec theta = root 8 / root 7

Now,

cosec ^2 theta - sec ^2 theta / cosec ^2 theta + sec ^2 theta

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