Examples of Math Problems: If sinx+cosx = 1/2, then tanx+cotx = ?

Saturday, June 22, 2013

If sinx+cosx = 1/2, then tanx+cotx = ?

we rewrite:

%0D%0Atanx%2Bcotx+=+sin%28x%29%2Fcos%28x%29%2Bsin%28x%29%2Fcos%28x%29%0D%0A

%0D%0Atanx%2Bcotx+=+sin%28x%29%2Fcos%28x%29%2Bsin%28x%29%2Fcos%28x%29%0D%0A

and after some algebra we can see that

%0D%0Atanx%2Bcotx=1%2F%28sin%28x%29cos%28x%29%29%0D%0A

%0D%0Atanx%2Bcotx=1%2F%28sin%28x%29cos%28x%29%29%0D%0A

Next we can square the given equation:

%0D%0Asin%28x%29%2Bcos%28x%29+=+1%2F2

%0D%0Asin%28x%29%2Bcos%28x%29+=+1%2F2

to get...

%0D%0Asin%5E2%28x%29%2B2sin%28x%29cos%28x%29%2Bcos%5E2%28x%29+=+1%2F4%0D%0A

and after simplifying we get
sin%28x%29cos%28x%29=-3%2F8

sin%28x%29cos%28x%29=-3%2F8

which means

%0D%0Atanx%2Bcotx=-8%2F3%0D%0A

%0D%0Atanx%2Bcotx=-8%2F3%0D%0A

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