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Prove that 2tan30upon1+tansquare30=sin60 |
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Answer» Ur short solution :-LHS = 2 tan 30÷1+tan²30......... Putting tan 30°= 1/√3............=> 2(1/√3) ÷ 1+ (1/√3)²..............=> 2/√3÷1+(1/3).............=> 2/√3÷4/3............=> 2/√3 * 3/4...........=> √3/2 = Sin 60°..........LHS = RHS ........HENCE PROVED. ANSWER!-LHS= 2 tan 30÷1+tan² 30...... Putting tan 30°=1/√3.....=> 2(1/√3)÷ 1+(1/√3)²......=> 2/√3÷1+(1/3)......=> 2/√3÷ 4/3 ( since taking LCM of 1+(1/3).....=> 2/√3* 3/4 ( while doing multiplication of both the reciprocal will happen of 4/3)...... Therefore, √3 n 3 will b cancelled and 3 becomes √3, 2 n 4 will b cancelled and 2 will remain......=> √3/2.......:. √3/2 = Sin 60°......LHS = RHS....... HENCE PROVED......I think i did my best to explain this solution better?.....yaa its seems to b lengthy bcuz i have solved plus explained also...... |
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