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Find the value of #sin30^@+cos30^@+tan30^@+cot30^@+sec30^@+csc30^@#?

Answer 1

Carter Anderson

#sin30^@+cos30^@+tan30^@+cot30^@+sec30^@+csc30^@=(5sqrt3)/2+1#

#sin30^@+cos30^@+tan30^@+cot30^@+sec30^@+csc30^@#

= #1/2+sqrt3/2+1/sqrt3+sqrt3+2/sqrt3+2#

= #(sqrt3+(sqrt3)^2+2+2(sqrt3)^2+4+sqrt3)/(2sqrt3)#

= #(sqrt3+3+2+6+4+sqrt3)/(2sqrt3)#

= #(15+2sqrt3)/(2sqrt3)#

= #(5sqrt3)/2+1#

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Answer 2

Caroline Adams

sin(30°) = 1/2 cos(30°) = √3/2 tan(30°) = 1/√3 cot(30°) = √3 sec(30°) = 2/√3 csc(30°) = 2

sin(30°) + cos(30°) + tan(30°) + cot(30°) + sec(30°) + csc(30°) = 1/2 + √3/2 + 1/√3 + √3 + 2/√3 + 2 = 2 + 2√3 + 2/√3 = 2 + 2√3 + (2√3)/3 = 2 + (8√3)/3

So, sin(30°) + cos(30°) + tan(30°) + cot(30°) + sec(30°) + csc(30°) = 2 + (8√3)/3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.