InterviewSolution
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InterviewSolution
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यदि `tan^(-1){(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2)))}=alpha`, तब सिद्ध कीजिए - `x^(2)=sin 2alpha.` |
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Answer» `tan^(-1){(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2)))}=tan alpha` `rArr" "=(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2)))=tan alpha` `rArr" "-(sqrt(1+x^(2)))/(sqrt(1-x^(2)))=(tan alpha+1)/(tan alpha-1),` [योगान्तरानुपात नियम से ] `rArr" "(sqrt(1-x^(2)))/(sqrt(1+x^(2)))=(1-tanalpha)/(1+tan alpha)` `rArr" "sqrt((1-x^(2))/(1+x^(2)))=(cos alpha-sinalpha)/(cos alpha+sin alpha)` `rArr" "(1-x^(2))/(1+x^(2))=((cos alpha-sin alpha)/(cos alpha+sin alpha))^(2)` `rArr" "(1+x^(2))/(1+x^(2))=(1-sin 2alpha)/(1+sin 2alpha)` `rArr" "x^(2)=sin 2alpha.` |
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