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यदि `x=(sqrt(3))/2` है तो `((sqrt(1+x)+sqrt(1-x))/(sqrt(1+x)-sqrt(1-x)))` का मान क्या होगा?A. `-sqrt(3)`B. `-1`C. `1`D. `sqrt(3)` |
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Answer» Correct Answer - D `x=(sqrt(3))/2` `(sqrt(1+x)+sqrt(1-x))/(sqrt(1+x)-sqrt(1-x))xx(sqrt(1+x)+sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))` `=((sqrt(1+x)+sqrt(1-x)^(2)))/((sqrt(1+x))^(2)-(sqrt(1-x))^(2))` `=(1+x+1-x+2sqrt(1-x^(2)))/(1+x-1+x)` `=(2+2sqrt(1-x^(2)))/(2x)=(1+sqrt(1-x^(2)))/x` `=(1+sqrt(1-3/4))/(sqrt(3))xx2` `=((1+1/2))/(sqrt(3))xx2=(3/2xx2)/(sqrt(3))=sqrt(3)` |
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