Question

24
Three Marks Questions
4. I 15 sin 0 = 8 cos 0, then find the value of
1+ sine
coto.
1-cos
ATT DTTMA
001AVKOVT​

Answer 1

$\rm Answer:-$

$\rm \dfrac{375}{16}$

$\rm Given :-$

$\rm 15sin\theta = 8cos\theta$

$\rm To \: Find :-$

$\rm \dfrac{1+sin\theta}{1-cos\theta} \times cot\theta$

$\rm Solution :-$

$\rm As \:they \: given\: that ,$

$\rm 15sin\theta = 8cos\theta$

$\rm So,$

$\rm \dfrac{sin\theta}{cos\theta} = \dfrac{8}{15}$

$\rm tan\theta = \dfrac{8}{15} [sinA/cosA= tanA]$

$\rm From \: this \: we \: can \: also \: find \: sin\theta , cos\theta , cot\theta$

$\rm tan\theta = \dfrac{opposite}{adjacent }$

$\rm So,$

$\rm Opposite\:side = 8 \\Adjacent side = 15$

$\rm From , Pythagoras \:Theorem, we\: can \: find \: Hypotenuse$

$\rm (opposite\:side)^2+(adjacent\:side)^2 = (Hypotenuse)^2$

$\rm (8)^2+(15)^2 = (Hypotenuse)^2$

$\rm 64+225 = (Hypotenuse)^2$

$\rm 289 = (Hypotenuse)^2$

$\rm (17)^2 = (Hypotenuse)^2$

$\rm Hypotenuse = 17$

$\rm As, \:we \: know \: that$

$\rm sin\theta = \dfrac{opposite}{hypotenuse}$

$\rm cos\theta =\dfrac{Adjacent}{Hypotenuse}$

$\rm cot\theta = \dfrac{adjacent}{opposite}$

$\rm Substituting \: the \: values$

$\rm sin\theta = \dfrac{8}{17}$

$\rm cos\theta =\dfrac{15}{17}$

$\rm cot\theta =\dfrac{15}{8}$

$\rm \dfrac{1+sin\theta}{1-cos\theta} \times cot\theta$

$\rm Substituting\: the\: values,$

$\rm \dfrac{1+\dfrac{8}{17} }{1-\dfrac{15}{17} }\times\dfrac{15}{8}$

$\rm \dfrac{\dfrac{17+8}{17} }{\dfrac{17-15}{17} } \times \dfrac{15}{8}$

$\rm \dfrac{\dfrac{25}{17} }{\dfrac{2}{17} } \times \dfrac{15}{8}$

$\rm\dfrac{25}{2} \times \dfrac{15}{8}$

$\rm \dfrac{25}{2} \times \dfrac{15}{8}$

$\rm \dfrac{375}{16}$

$\rm So,\: the \: value \:of \rm \dfrac{1+sin\theta}{1-cos\theta} \times cot\theta \:is\dfrac{375}{16}$

$\rm Know\:more:-$

$\rm Trigonometric \:Identities :-$

$\rm sin^2A +cos^2A = 1$

$\rm sec^2A - tan^2A = 1$

$\rm csc^2A - cot^2A =1$

$\rm Trigonometric \:relations:-$

$\rm sinA = 1/cscA$

$\rm cosA = 1 /secA$

$\rm tanA= 1/cotA$

$\rm tanA = sinA/cosA$

$\rm cotA = cosA/sinA$

$\rm Trigonometric \:ratios:-$

$\rm sinA = opp/hyp$

$\rm cosA = adj/hyp$

$\rm tanA= opp/adj$

$\rm cotA = adj/opp$

$\rm cscA = hyp/opp$

$\rm secA = hyp/adj$