Question

pls..... help me....................!!!!!!!!!!!??!!!????

Answer 1

15). tan + cot = 5

On squaring both side

$(tan + cot) {}^{2} = 5 {}^{2}$

$tan {}^{2} + cot {}^{2} + 2tan.cot = 25$

$tan.cot = 1$

$tan {}^{2} + cot {}^{2} = 25 - 2 = 23$

$tan {}^{2} + cot {}^{2} = 23$


14) let length of rope is = h

height of tower is= p

distance from tower to rope = b

sin theta = p / h

sin30° = 2 / h

1/2 = 2/h

h = 4m

Length of rope is 4m.


Thanks

Answer 2

Hope u like my process
======================
14)

=> Height of tower (p) = 2 m

=> Let length of rope be h m

=> Angle made = 30 °
_______________________

So, by problem
=-=-=-=-=-=-=-=-=-=

$= > \sin( \theta) = \frac{p}{h} \\ \\ or. \: \: \sin(30) = \frac{2}{h} \\ \\ or. \: \: h \times \frac{ 1 }{2} = 2 \\ \\ or. \: \bf \: h = \underline{1}$
So,
The length of rope is 1 m
____________________________
15)

$= > \tan( \theta ) + \cot( \theta ) = 5 \\ \\ \bf \underline{squaring \: \: both \: \: sides..} \\ \\ = > ({ \tan( \theta ) + \cot( \theta ) )}^{2} = {5}^{2} \\ \\ or. \: \: \tan ^{2} ( \theta ) + \cot ^{2} ( \theta ) + 2 \tan( \theta ) \cot( \theta) = 25 \\ \\ or. \: \: \tan ^{2} ( \theta ) + \cot ^{2} ( \theta ) = 25 - 2 \\ \\ or. \bf \: \: \tan ^{2} ( \theta ) + \cot ^{2} ( \theta) = \underline{23}$
____________________________
16)


Hope u like my process
=====================

$= > \bf2 \sin( \theta ) - \cos( \theta ) = 2 \\ \\ \bf \underline{squaring \: \: both \: \: sides \: \: } \\ \\ = > \: {(2 \sin( \theta ) - \cos( \theta ) )}^{2} = {2}^{2} \\ \\ or. \: \: 4 \sin ^{2} ( \theta ) + \cos ^{2} ( \theta ) - 4 \sin( \theta ) \cos( \theta ) = 4 \\ \\ or. \: \: 4(1 - \cos ^{2} ( \theta ) ) + (1 - \sin ^{2} ( \theta ) ) - 4 \sin( \theta) \cos( \theta ) = 4 \\ \\ or. \: \: 4 - 4 \cos ^{2} ( \theta ) + 1 - \sin ^{2} ( \theta ) - 4 \sin( \theta ) \cos( \theta ) = 4 \\ \\ or. \: \: 4 \cos ^{2} ( \theta ) + \sin ^{2} ( \theta ) + 4 \sin( \theta ) \cos( \theta ) = 1 \\ \\ or. \: \: {( \sin( \theta ) + 2\cos( \theta )) }^{2} = {1}^{2} \\ \\ or. \: \: \bf \: \sin( \theta ) + 2 \cos( \theta ) = \sqrt{1} = \underline{1}$
___________________________
Hope this is ur required answer

Proud to help you