I think you can use one of the sum and difference identities formulas for this one
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Sec(pi/2-u)= 1/cos(pi/2-u)
1/cos(pi/2-u) = 1/sin(u)
1/sin(u)= csc(u)
Therefore, Sec(pi/2-u) = csc(u)
1/cos(pi/2-u) = 1/sin(u)
1/sin(u)= csc(u)
Therefore, Sec(pi/2-u) = csc(u)
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This is a specific case of the rule: "co-functions of complements are equal".
Remember that the co-functions are:
sin and co-sine
tan and co-tan
sec and co-sec
Remember that u and π/2 - u are complements, since they add to π/2, i.e. their sum is 90 degrees.
The fact that co-functions of complements are equal follows from the definition of the functions in a right triangle, and that opp and adj sides swap if you move focus from one acute angle to the other.
Remember that the co-functions are:
sin and co-sine
tan and co-tan
sec and co-sec
Remember that u and π/2 - u are complements, since they add to π/2, i.e. their sum is 90 degrees.
The fact that co-functions of complements are equal follows from the definition of the functions in a right triangle, and that opp and adj sides swap if you move focus from one acute angle to the other.
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Recall that cos(π/2 - u) = sin(u) is an identity. If you express sec and csc in terms of sin and cos, it falls out very easily.
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all are positive in the first quadrant
π/2 =90deg
sec( 90deg - x) = cosecx
thus sec(π/2 - u) = csc u
π/2 =90deg
sec( 90deg - x) = cosecx
thus sec(π/2 - u) = csc u