Question

if cos theta is equal to 7 by 8 evaluate 1 + sin theta into 1-sin theta by 1 + cos theta into 1- cos theta.

Answer 1

Solution

→ cos∅ = 7/8

To Evaluate: (1 + sin∅)(1 - sin∅)/(1 + cos∅)(1 - cos∅)

→ (1² - sin²∅)/(1² - cos²∅)

→ (1 - sin²∅)/(1 - cos²∅)

We know that 1 - sin²∅ = cos²∅

→ cos²∅/(1 - cos²∅)

→ (7/8)²/{1 - (7/8)²}

→ (49/64)/(1 - 49/64)

→ (49/64)/(64 - 49)/64

→ 49/64 × 64/15

→ 49/15

Required answer is 49/15

Answer 2

$\huge{\mathfrak{\red{\underline{\underline{Answer :-}}}}}$

49/15

$\large{\mathrm{\gray{Given :-}}}$

Cos ∅ = 7/8

$\large{\mathrm{\gray{To \: Find :-}}}$

$\LARGE{\frac{(1 + \sin \theta)(1 - \sin \: \theta)}{(1 + \cos \theta)(1 - \cos\theta)}}$

Using Identity :-

$\LARGE{\boxed{\boxed{\bf{\red{(a + b)(a - b) = a^{2} - b^{2}}}}}}$

$\frac{( 1- { \sin}^{2}{ \theta}) }{( 1- { \cos}^{2}{ \theta}) } \\ \\ \bf{we \: know \: that} \\ \\ \pink {\boxed{(1- { \sin}^{2}{ \theta}) = { \cos}^{2} \theta}} \\ \\ \frac{ { \cos}^{2} \theta}{1 - { \cos}^{2} \theta } \\ \\ \bf{put \: values}$

» (7/8)² / (1 - 7/8)²

By taking LCM

» (49/64) / (64 - 49) / 64

» 49/64 * 64 / 15

» 49 / 15

$\large{\boxed{\boxed{\bf{\red{\frac{49}{15}}}}}}$

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