Question

can any one say this answer​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

We are aware of the Trigonometric identity that

1.

$1 + {tan}^{2} \theta \: = {sec}^{2} \theta$

2.

${sin}^{2} \theta = 1 - {cos}^{2} \theta$

TO PROVE

$\displaystyle \: (1 + {tan}^{2} \theta \: )(1 + \frac{1}{ {tan}^{2} \theta \: }) = = \displaystyle \: \frac{1}{{sin}^{2} \theta - \: {sin}^{4} \theta\: } \:$

CALCULATION

$\displaystyle \: (1 + {tan}^{2} \theta \: )(1 + \frac{1}{ {tan}^{2} \theta \: })$

$= \displaystyle \: {sec}^{2} \theta \: \times \frac{(1 + {tan}^{2} \theta \: ) }{ {tan}^{2} \theta \: }$

$= \displaystyle \: {sec}^{2} \theta \: \times \frac{{sec}^{2} \theta \: }{ {tan}^{2} \theta \: }$

$= \displaystyle \: \frac{1}{{cos}^{2} \theta} \: \times \frac{1}{{cos}^{2} \theta} \: \times \frac{{cos}^{2} \theta \: }{ {sin}^{2} \theta \: }$

$= \displaystyle \: \frac{1}{{cos}^{2} \theta} \: \times \frac{1}{{sin}^{2} \theta} \:$

$= \displaystyle \: \frac{1}{1 - {sin}^{2} \theta} \: \times \frac{1}{{sin}^{2} \theta} \:$

$= \displaystyle \: \frac{1}{{sin}^{2} \theta - \: {sin}^{4} \theta\: } \:$