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Trigonometric Questions Dealing with Identities PART I
The following are questions that you may see using your trig identities.
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What is the value of 1-sin2(2x) if cos2(x)=1 in the domain [0,π]?
You could use the half angle formula, but cos2(x)=1 when x=0 and that is the only time. If you double the angle 0, then it will still be zero, so the answer is 1.
Without the use of a calculator, find the value of -(sinx+cosx)(sinx-cosx) given that x=15 degrees.
a. Expand and you get -(sin2x-cos2x)=-sin2x+cos2x=cos(2x)=cos(2(15))=cos(30)= square root of three divided by 2
Note: √ represents square root
Given √(1-sin2x)(2/√(1+cot2x)), what is the value of this expression when x=15 degrees (no calculator allowed).
square root of all(1-sin2x) and square root of all (1+cot2x)
a. (1-sin2x)=cos2x, square root of this is simply cosx
b. (1+cot2x)=cscx, 2/cscx=2sinx because cscx=1/sinx and 1/(1/sinx)=sinx
Now the product is 2sinxcosx=sin2x=sin(2(15))=sin30=1/2