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| 1. |
If 6x=sec& 6÷x=tan& & = t ratio ( thita) |
| Answer» We have,6x = sec\xa0{tex}\\theta{/tex}........(i)and\xa0{tex}\\frac { 6 } { x } = \\tan \\theta{/tex} ........(ii)Adding (i) and (ii), we get{tex}6 \\left( x + \\frac { 1 } { x } \\right) = ( \\sec \\theta + \\tan \\theta ){/tex}.......(iii)Subtracting (ii) from (i), we get{tex}6 \\left( x - \\frac { 1 } { x } \\right) = ( \\sec \\theta - \\tan \\theta ){/tex}........(iv)Multiplying the corresponding sides of (iii) and (iv), we get{tex}36 \\left( x ^ { 2 } - \\frac { 1 } { x ^ { 2 } } \\right) = \\left( \\sec ^ { 2 } \\theta - \\tan ^ { 2 } \\theta \\right) = 1{/tex}{tex}\\Rightarrow 9 \\left( x ^ { 2 } - \\frac { 1 } { x ^ { 2 } } \\right) = \\frac { 1 } { 4 }{/tex} | |