SOLUTION: USE IDENTITY TO FIND THE VALUE OF EACH EXPRESSION. DO NOT USE A CALCULATOR (ANSWER MUST IN RADICAL FORM, NOT DECIMALS) (a) cos 53(degree)sec53(degree) (b)sin^2(pi/10)+cos^2(pi/

Algebra ->  Trigonometry-basics -> SOLUTION: USE IDENTITY TO FIND THE VALUE OF EACH EXPRESSION. DO NOT USE A CALCULATOR (ANSWER MUST IN RADICAL FORM, NOT DECIMALS) (a) cos 53(degree)sec53(degree) (b)sin^2(pi/10)+cos^2(pi/      Log On


   

Question 852881: USE IDENTITY TO FIND THE VALUE OF EACH EXPRESSION. DO NOT USE A CALCULATOR (ANSWER MUST IN RADICAL FORM, NOT DECIMALS)
(a) cos 53(degree)sec53(degree)
(b)sin^2(pi/10)+cos^2(pi/10)
(c)csc63(degree)-cot63(degree)
Please I really need these exercises. Thank you! :)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)

By definition, sec(x) = 1/cos(x)

So,

cos(53)*sec(53) = cos(53)*1/(cos(53)) = cos(53)/cos(53) = 1

In short, cos(53)*sec(53) = 1

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b)

The Pythagorean Trig Identity is: sin^2(x)+cos^2(x) = 1

This is true for any real value x. That means

sin^2(pi/10)+cos^2(pi/10) = 1

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c)

csc(63) - cot(63)


1/sin(63) - cos(63)/sin(63)


(1 - cos(63))/sin(63)


This is as far as I'm getting. I'm not able to find a result in radical form. So there might be a typo somewhere.