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If 6x=secA and 6/x=tanA then find …

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If 6x=secA and 6/x=tanA then find value of 9(x^2-1/x^2)

Posted by Gautam Sharma 6 years ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years ago

We have,
6x = sec $\theta$ ........(i)
and $\frac { 6 } { x } = \tan \theta$ ........(ii)
Adding (i) and (ii), we get
$6 \left( x + \frac { 1 } { x } \right) = ( \sec \theta + \tan \theta )$ .......(iii)
Subtracting (ii) from (i), we get
$6 \left( x - \frac { 1 } { x } \right) = ( \sec \theta - \tan \theta )$ ........(iv)
Multiplying the corresponding sides of (iii) and (iv), we get
$36 \left( x ^ { 2 } - \frac { 1 } { x ^ { 2 } } \right) = \left( \sec ^ { 2 } \theta - \tan ^ { 2 } \theta \right) = 1$
$\Rightarrow 9 \left( x ^ { 2 } - \frac { 1 } { x ^ { 2 } } \right) = \frac { 1 } { 4 }$

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