Find the value of the expression sec9-4tan-9-4-

Given: nbsp;sec(9π4)tan( 9π4) 9π4 nbsp; nbsp;= nbsp;2π+π4⇒sec(9π4)tan( 9π4) nbsp;= nbsp;sec(9π4)( tan(9π4)) nbsp; nbsp; nbsp; nbsp; nbsp; ...

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Standard XII

Mathematics

Trigonometric Ratios Using Right Angled Triangle

Find the valu...

Question

Find the value of the expression $sec (\frac{9 π}{4}) tan (- \frac{9 π}{4}) .$

\sqrt{2}

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- \sqrt{2}

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\frac{1}{\sqrt{2}}

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- \frac{1}{\sqrt{2}}

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Solution

The correct option is B $- \sqrt{2}$
Given: $sec (\frac{9 π}{4}) tan (- \frac{9 π}{4})$
$\frac{9 π}{4} = 2 π + \frac{π}{4} \Rightarrow sec (\frac{9 π}{4}) tan (- \frac{9 π}{4}) = sec (\frac{9 π}{4}) (- tan (\frac{9 π}{4})) = sec (2 π + \frac{π}{4}) (- tan (2 π + \frac{π}{4})) = sec (\frac{π}{4}) (- tan (\frac{π}{4})) = (\sqrt{2}) (- 1) = - \sqrt{2}$

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Find the value of the expression sec(9π4)tan(−9π4).

The correct option is B −√2Given: sec(9π4)tan(−9π4) 9π4 = 2π+π4⇒sec(9π4)tan(−9π4) = sec(9π4)(−tan(9π4)) = sec(2π+π4)(−tan(2π+π4)) = sec(π4)(−tan(π4)) = (√2)(−1) = −√2

Find the value of the expression $sec (\frac{9 π}{4}) tan (- \frac{9 π}{4}) .$