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| Multiplication of Tangent |
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| Find [tan(a)+1]*[tan(b)+1] if a+b=45deg where a,b<45deg Solution : a=45-b tan(a)=tan(45-b) tan(a)=[tan(45)-tan(b)]/[1+tan(45)*tan(b)] tan(a)=[1-tan(b)]/[1+tan(b)] multiply both sides by [1+tan(b)] tan(a)*[1+tan(b)]=1-tan(b) tan(a)*[1+tan(b)]+tan(b)=1 add both sides by 1 : tan(a)*[1+tan(b)+[1+tan(b)]=1+1 [1+tan(b)]*[tan(a)+1]=2 [1+tan(a)]*[1+tan(b)]=2 is the final answer |
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