Question

Verify the identity. Justify each step. tan (thetA) + cot (thetA) = 1 / sin (thetA) cos (thetA)

Answer 1

theta = t
tan t + cot t = 1/ sin t cos t
sin t / cos t + cos t / sin t = 1 / sin t cos t
( sin² t + cos² t ) / sin t cos t = 1/ sin t cos t
1/ sin t cos t = 1 / sin t cos t 

Answer 2

The verification of the given identity i.e. an (thetA) + cot (thetA) = 1 / sin (thetA) cos (thetA) so it should be explained below.

Verification of the identity:

Since

theta = t

tan t + cot t = 1/ sin t cos t

Now

sin t / cos t + cos t / sin t = 1 / sin t cos t

So,

( sin² t + cos² t ) / sin t cos t = 1/ sin t cos t

And, finally

1/ sin t cos t = 1 / sin t cos t

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