Question

Given that tan(A-B)= tanA-tanB/1+tanatanb find the value of 30° by taking suitable values of A and B​

Answer 1

tan (75) = tan (30 + 45) \\ tan (30 + 45) = \ frac {tan30 + tan45} {1-tan30.tan45} \\ = \ frac {(frac {1}} {\ sqc {} 3}} +1)} {1- \ frac {1} {\ sqrt {3}} .1} \\ = \ frac {\ frac {1+ \ sqrt {3}} {\ sqrt {3}}} {{frac {\ sqrt {3} -1} {\ sqrt {3}}} \\ tan75 = \ frac {\ sqrt {3} +1} {\ sqrt {3} -1}

अब, टैन (90) = टैन (45 + 45)

tan (45 + 45) = \ frac {tan45 + tan45} {1-tan45.tan45} \\ = \ frac {1 + 1} {1-1 * 1} = \ frac {1} {0}

= अनंत