Given #csctheta^circ=sqrt3/2# and #sectheta^circ=sqrt3/3#, how do you find #sec(90^circ-theta)#?

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Answer 1 · 2016-12-19T05:53:14

There is no solution.

#sin theta = 1/(csc theta)#

#sin theta = 2/sqrt3 = 2/1.73 #

#= 1.15 > 0#

Therefore, there is no such angle #theta# that has sin > 1.

Answer 2 · 2016-12-19T07:11:33

There is no such angle #theta# and we do not have a solution.

As the trigonometric ratios cosecant and secant cannot have their absolute value less than one

i.e. #|csctheta|>=1# and #|sectheta|>=1#

However, here #csctheta=sqrt3/2=1.732/2=0.866<1#

and #sectheta=sqrt3/3=1.732/3=0.5773<1#

There is no such angle #theta# and we do not have a solution.