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Evaluate: tan105deg using the sum and difference formulas.
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akash_809
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tan(a+b)=(tan a +tan b)/(1-tan a tan b)....put a =60 and b =45 and solve
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where u got 60 and 45?
akash_809
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tan(60+45)=tan105...right
akash_809
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can u do it nw
akash_809
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tan 60 =\[\sqrt{3}\] and tan 45 =1
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i am getting stuck at the part where it is: |dw:1347964171044:dw|
akash_809
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so \[\tan105= (1+\sqrt{3})/(1-\sqrt{3}) \]
akash_809
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|dw:1347964267571:dw|
akash_809
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can u solve this now
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wait. why did you square that?
akash_809
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|dw:1347965085424:dw|
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arent you suppposed to mutliply it by the bottom one?
akash_809
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no it is rationalization u multiply num and den both by a coomon value so that the expression remains unaffected
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so it is always the numerator?
akash_809
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no depends on what simplifies the root if 1-root 3 was there in numerator and 1+root 3 in den the you would multiply num and den by 1-root 3...since (1+root 3)(1-root3)=1-3...using a^2-b^2
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how would you know which one to multiply by tho?
akash_809
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multiply with a value that would make denominator a rational one