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If `tantheta=sqrt(m)`, where m is non-square natural number, then sec `2theta` isA. a negative numberB. a transcendental numberC. an irrational numberD. a rational number |
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Answer» Correct Answer - A Let `tan theta=sqrt(m)`, where m is a non-square natural number. `implies sin theta=sqrt(m) cos theta` Consider, `sec2theta=(1)/(cos2theta)=(1)/(cos^(2)theta-sin^(2)theta)` `=(1)/(cos^(2)theta-mcos^(2)theta)=(1)/(cos^(2)theta(1-m))` `=(sec^(2)theta)/(1-m)=(1+tan^(2)theta)/(1-m)=(1+m)/(1-m)` `=((1+m)(1-m))/((1-m)(1-m))=((1-m^(2)))/((1-m)^(2))` Numerator will always be negative and denominator will always be positive. Hence, `sec2theta=(1-m^(2))/((1-m)^(2))` is a negative number. |
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