Verify the identity tan t sin t sec2 t 1sec t Which of the

Verify the identity. tan t sin t = sec^2 t - 1/sec t Which of the following three statements establishes the identity? A. tan t sin t = tan t (tan t/sec t) = sec^2 t - 1/sec t B. tan t sin t = tan t (sec t/tan t) = sec^2 t - 1/sec t C. tan t tan t (cot t/cos t) = sec^2 t - 1/sec t

Solution

tan t sin t = (sec^2 t - 1) / sec t

sin t can be written as

tan t / sec t

as tan t = sin t / cos t and sec t = 1/ cos t

so we get

tan t ( tan t / sec t )

= tan^2 t / sec t

and tan^2 t = sec^2 t -1

hence, it becomes

sec^2 t -1 / sec t

which is right side

option a is correct