Question

From the figure (2) given below, find the values of:
(i) tan x (ii) cos y (iii) cosec2 y - cot2y (iv)5/sin x+3/sin y-3 cot y
please give me the answers as quick as possible please​

Answer 1

Answer:

(i) tan x = 5/12

(ii) cos y = 16/20

(iii) cosec2 y - cot2y  = 1

iv) 5/sin x+3/sin y-3 cot y   = -22/5

Step-by-step explanation:

AD = $\sqrt{AC^{2} - DC^{2} }$ = $\sqrt{(13^{2} - 5^{2})}$ = $\sqrt{169 - 25}$ = $\sqrt{144}$ = 12

DC = 5

BD = 21-5 = 16

AB = $\sqrt{AD^{2} + BD^{2} }$ = $\sqrt{(12^{2} + 16^{2})}$ = $\sqrt{144 + 256}$ = $\sqrt{400}$ = 20

BC = 21

AC = 13

------------------------------

(i) tan x = DC / AD = 5/12

-----------

(ii) cos y = BD/AB = 16/20

--------------

(iii) cosec2 y - cot2y

= $\frac{1}{sin^{2} y}$ - $\frac{cos^{2} y}{sin^{2} y}$

= $\frac{1-cos^{2}y }{sin^{2} y}$ = $\frac{sin^{2} y}{sin^{2} y}$

= 1

-------------

(iv)5/sin x+3/sin y-3 cot y  

= $\frac{5}{sinx}$ + $\frac{3}{siny}$ - $\frac{3*cosy}{siny}$

= $\frac{5*siny + 3*sinx - 3*cosy}{sinx * siny}$

= (5*AD/AB + 3*DC/AC - 3*BD/AB) / (DC/AC * AD/AB)

= (5*12/20 + 3*5/13 - 3* 16/20) / 5/13 * 12/20

= (60/20 + 15/13 - 48/20) / 60/260

= -22/5

Answer 2

Step-by-step explanation:

Answer:

(i) tan x = 5/12

(ii) cos y = 16/20

(iii) cosec2 y - cot2y = 1

iv) 5/sin x+3/sin y-3 cot y = -22/5

Step-by-step explanation:

AD = \sqrt{AC^{2} - DC^{2} }

AC

2

−DC

2

= \sqrt{(13^{2} - 5^{2})}

(13

2

−5

2

)

= \sqrt{169 - 25}

169−25

= \sqrt{144}

144

= 12

DC = 5

BD = 21-5 = 16

AB = \sqrt{AD^{2} + BD^{2} }

AD

2

+BD

2

= \sqrt{(12^{2} + 16^{2})}

(12

2

+16

2

)

= \sqrt{144 + 256}

144+256

= \sqrt{400}

400

= 20

BC = 21

AC = 13

------------------------------

(i) tan x = DC / AD = 5/12

-----------

(ii) cos y = BD/AB = 16/20

--------------

(iii) cosec2 y - cot2y

= \frac{1}{sin^{2} y}

sin

2

y

1

- \frac{cos^{2} y}{sin^{2} y}

sin

2

y

cos

2

y

= \frac{1-cos^{2}y }{sin^{2} y}

sin

2

y

1−cos

2

y

= \frac{sin^{2} y}{sin^{2} y}

sin

2

y

sin

2

y

= 1

-------------

(iv)5/sin x+3/sin y-3 cot y

= \frac{5}{sinx}

sinx

5

+ \frac{3}{siny}

siny

3

- \frac{3*cosy}{siny}

siny

3∗cosy

= \frac{5*siny + 3*sinx - 3*cosy}{sinx * siny}

sinx∗siny

5∗siny+3∗sinx−3∗cosy

= (5*AD/AB + 3*DC/AC - 3*BD/AB) / (DC/AC * AD/AB)

= (5*12/20 + 3*5/13 - 3* 16/20) / 5/13 * 12/20

= (60/20 + 15/13 - 48/20) / 60/260

= -22/5