If θ is an acute angle and tan θ=17, then the value of cosec2θ-sec2θcosec2θ+sec2θ is

tan θ=17and sec θ=17cosec θ=1cosec2θ-sec2θcosec2θ+sec2θ = (1)2-172(1)2+172 =1-171+17 =6787 =68=34

If θ is an acute angle and tan θ=17, then the value of cosec2θ-sec2θcosec2θ+sec2θ is

tan θ=17and sec θ=17cosec θ=1cosec2θ-sec2θcosec2θ+sec2θ = (1)2-172(1)2+172 =1-171+17 =6787 =68=34

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If $θ$ is an acute angle and $\tan θ = \frac{1}{\sqrt{7}}$ , then the value of $\frac{\cos e c^{2} θ - s e c^{2} θ}{\cos e c^{2} θ + s e c^{2} θ}$ is

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$\frac{3}{4}$

$\frac{1}{2}$

5/4

answer is A.

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Detailed Solution

$\tan θ = \frac{1}{\sqrt{7}}$ and $s e c θ = \frac{1}{\sqrt{7}}$ $\cos e c θ = 1$

$\frac{\cos e c^{2} θ - s e c^{2} θ}{\cos e c^{2} θ + s e c^{2} θ} = \frac{(1)^{2} - {(\frac{1}{\sqrt{7}})}^{2}}{(1)^{2} + {(\frac{1}{\sqrt{7}})}^{2}} = \frac{1 - \frac{1}{7}}{1 + \frac{1}{7}} = \frac{\frac{6}{7}}{\frac{8}{7}} = \frac{6}{8} = \frac{3}{4}$