SOLUTION: if tan theta equals cot theta then value of sec theta will be ??

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Question 880280: if tan theta equals cot theta then value of sec theta will be ??
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
(1) tan(x) = cot(x) or
(2) tan(x) = 1/tan(x) or
(3) tan%5E2%28x%29+=+1
Use the well known identity
(4) sin%5E2%28x%29+%2B+cos%5E2%28x%29+=+1 (If you don't know it memorize it).
we can, by dividing through by cos%5E2%28x%29, derive another identity
(5)sin%5E2%28x%29%2Fcos%5E2%28x%29+%2B+1+=+1%2Fcos%5E2%28x%29 or
(6)tan%5E2%28x%29+%2B+1+=+sec%5E2%28x%29
Using the given value of tan%5E2%28x%29+=+1 in (3) we have
(7)1+%2B+1+=+sec%5E2%28x%29 or
(8)2+=+sec%5E2%28x%29 or
(9))sec%28x%29+=+sqrt%282%29
The answer of (9) can easily be verified using the 45 degree right triangle given by (3).