Question

if 2 tan theta is equal to 3 find the value of sec square theta minus one upon cot theta ​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

The value of given expression is $\frac{7}{4}$.

Step-by-step explanation:

2tan$\theta$ = 3

=> tan$\theta$ = $\frac{3}{2}$

Here, p = 3 and b = 2

By using pythagorean theorem,

h = $\sqrt{p^{2} +b^{2} }$ = $\sqrt{3^{2} + 2^{2} } = \sqrt{9+4} =\sqrt{13}$

sec$\theta$ = $\frac{h}{b}$ = $\frac{\sqrt{13} }{2}$

cot$\theta$ = $\frac{b}{p} = \frac{2}{3}$

Now, $sec^{2} \theta- \frac{1}{cot\theta}$

= $(\frac{\sqrt{13}}{2}) ^{2} - \frac{1}{\frac{2}{3}}$

= $\frac{13}{4} - \frac{3}{2}$

= $\frac{13-6}{4}$

= $\frac{7}{4}$

Hence, the value of given expression is $\frac{7}{4}$.