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1). 12). π/23). 5/24). None of these |
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Answer» We have, sin θ = 21/29 $(\Rightarrow {\RM{cos\theta }} = \sqrt {1 - {{\sin }^2}{\rm{\theta }}} = {\rm{\;}}\sqrt {1 - {{\left( {\FRAC{{21}}{{29}}} \RIGHT)}^2}} = {\rm{\;}}\sqrt {({{29}^2} - {{21}^2})/\left( {{{29}^2}} \right)} = \sqrt {\frac{{8 \times 50}}{{{{29}^2}}}} = {\rm{\;}}\frac{{20}}{{29}}{\rm{\;}})$ [We take only positive value of cos because θ lies between 0 and π/2] Now, $(\sec {\rm{\theta \;}} + {\rm{\;tan\theta }} = {\rm{\;}}\frac{1}{{{\rm{cos\theta }}}}{\rm{\;}} + {\rm{\;}}\frac{{{\rm{sin\theta }}}}{{{\rm{cos\theta }}}} = {\rm{\;}}\frac{{1{\rm{\;}} + {\rm{\;sin\theta }}}}{{{\rm{cos\theta }}}} = {\rm{\;}}\frac{{1{\rm{\;}} + {\rm{\;}}\frac{{21}}{{29}}}}{{\frac{{20}}{{29}}}} = {\rm{\;}}\frac{{50}}{{20}} = {\rm{\;}}\frac{5}{2})$ |
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