Question

Proof :

1/1+ sin theta + 1/1-sin theta = 2 sec square theta

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Answer 1

Step-by-step explanation:

1/(1-sintheta) + 1/(1+sintheta)

= (1+sintheta+1-sintheta)/(1+sintheta)(1-sintheta)

=2/1-sin²theta

=2/cos²theta = 2sec²theta

Answer 2

$\bf\large\blue{Question\::-}$

$\text{Proof that :}$

$\frac{1}{1 + \: \sin \theta} + \frac{1}{1 - \: \sin \theta} = 2 \: { \sec}^{2} \theta$

$\bf\large\blue{Solution\::-}$

$\underline{L.H.S}$

$\frac{1}{1 + \: \sin \theta} + \frac{1}{1 - \: \sin \theta} = 2 \: { \sec}^{2} \theta$

$= \frac{1 \: - \: \cancel{ \sin \theta } + \: 1 \: + \: \cancel{ \sin \theta}}{(1 \: + \: \sin \theta )(1 \: - \: \sin \theta)}$

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

$\text{We know, }$$1 - { \sin}^{2} \theta = {\cos}^{2}\theta$

$\text{Then,}$

$\frac{2}{ { \cos}^{2} \theta}$

$= \frac{2}{ \frac{1}{ \sec ^{2} \theta} }$

$= 2 \: \sec ^{2} \theta \: = R.H.S$

$\bf\large\blue{Hence \: proved \:.}$

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