SOLUTION: Evaluate Sec 660degrees + Cot 405degrees without using a calculator. Please show steps thanks you!

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Question 1154166: Evaluate Sec 660degrees + Cot 405degrees without using a calculator. Please show steps thanks you!
Found 3 solutions by josgarithmetic, Alan3354, MathLover1:
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website!
Do you realize that 405 degrees is 9 times 45 degrees?
Do you realize that 660 degrees is 11 times 60 degrees?

Make reference to the common angles on the unit circle, and take the values for sec(660) and cot(405) that way, and do your computations.

Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
Evaluate Sec 660degrees + Cot 405degrees
------
Subtract 360
= sec(300) + cot(45)
= 1/cos(300) + 1
= 1/cos(60) + 1
= 2 + 1
= 3

Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!

..........express with sin and cos

=..use identity: ..since your

=

...........use the following property :

=

rewrite .......... apply the periodicity of sin :

so,

=................rewrite the angles for =

=......write as

using the summation identity :

so you have

now use the following trivial identities:

then you have
and

so, you have:

=
=
=
=>