Answer:
Explanation:
The question is incorrect. Here is the correct question.
Verify the identity sin²t / cos t = sect - cost
Given the identity sin²t / cos t = sect - cost, to verify means we are to check if both sides are equivalent. To do that we are going to start the proof from any sides of the equation and solve until we get to the function at the opposite side.
Starting with the left hand equation (LHS)
sin²t / cos t ...1
From trigonometry identity, sin²t+ cos²t = 1
sin²t = 1- cos²t ... 2
Substituting eqn 2 into 1 we have:
= 1- cos²t/cost
= 1/cost - cos²t/cost
= 1/cost - cost
Also from trig. identity, 1/cost = sect
On replacing this identity in the resulting equation we will have;
= sect - cost (which is equivalent to the RHS)
This shows that sin²t / cos t = sect - cost (Identity Proved!)