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Prove that 2tan30upon1+tansquare30=sin60

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Prove that 2tan30upon1+tansquare30=sin60

Posted by Simba Sikarwar 5 years ago

CBSE > Class 10 > Mathematics

2 answers

Sakshi Jagtap 5 years ago

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.

Sakshi Jagtap 5 years ago

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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