InterviewSolution
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InterviewSolution
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यदि `cos^(-1)""(x)/(a)+cos^(-1)""(y)/(b)=theta` तो सिद्ध कीजिए कि `(x^(2))/(a^(2))-(2xy)/(ab).costheta+(y^(2))/(b^(2))=sin^(2)theta`. |
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Answer» `cos^(-1)""(x)/(a)+cos^(-1)""(y)/(b)=theta` `impliescos^(-1)[(x)/(a).(y)/(b)-sqrt(1-(x^(2))/(a^(2)))sqrt(1-(y^(2))/(b^(2)))]=theta` `implies(xy)/(ab)-sqrt(1-x^(2)/(a^(2))-y^(2)/(b^(2))+(x^(2)y^(2))/(a^(2)b^(2)))=costheta` `implies(xy)/(ab)costheta=sqrt(1-(x^(2))/(a^(2))-(y^(2))/(b^(2))+(x^(2)y^(2))/(a^(2)b^(2)))` दोनों पक्षों का वर्ग करने पर `(x^(2)y^(2))/(a^(2)b^(2))+cos^(2)theta-(2xy)/(ab)costheta=1-(x^(2))/(a^(2))-(y^(2))/(b^(2))+(x^(2)y^(2))/(a^(2)b^(2))` `implies(x^(2))/(a^(2))-(2xy)/(ab)costheta+(y^(2))/(b^(2))=1-cos^(2)theta` `implies(x^(2))/(a^(2))-(2xy)/(ab)costheta+(y^(2))/(b^(2))=sin^(2)theta` |
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