Question

Class 10th//Maths (Trigonometry)
Answer with proper explanation.​

Answer 1

Answer:

OPTION B IS CORRECT.

Step-by-step explanation:

$\cot(a + b - c) = 1 \\ \\ a + b - c = 45 \: \: \: ...(i) \\ \\ \csc(b + c - a) = 2 \\ \\ b + c - a = 30 \: \: \: \: \: \: \: \: \: ...(ii) \\ \\ solving \: these \: \: \: we \: get \\ \\ 2b = 75 \\ \\ b = \frac{75}{2} \\ \\ a - c = 45 - \frac{75}{2} \\ \\ a - c = \frac{15}{2} \\ \\ \\ \\ by \: angle \: sum \: property \\ \\ a + b + c = 180 \\ \\ a + c = 180 - \frac{75}{2} \\ \\ a + c = \frac{360 - 75}{2} \\ \\ a + c = \frac{285}{2} \\ \\ therefore \: \: \: \: \: \: \: 2a =1 50 \\ \\ a = 75 \\ \\ c = \frac{285}{2} - \frac{75}{1} \\ \\ c = \frac{135}{2} .$

Answer 2

Step-by-step explanation:

\begin{gathered} \cot(a + b - c) = 1 \\ \\ a + b - c = 45 \: \: \: ...(i) \\ \\ \csc(b + c - a) = 2 \\ \\ b + c - a = 30 \: \: \: \: \: \: \: \: \: ...(ii) \\ \\ solving \: these \: \: \: we \: get \\ \\ 2b = 75 \\ \\ b = \frac{75}{2} \\ \\ a - c = 45 - \frac{75}{2} \\ \\ a - c = \frac{15}{2} \\ \\ \\ \\ by \: angle \: sum \: property \\ \\ a + b + c = 180 \\ \\ a + c = 180 - \frac{75}{2} \\ \\ a + c = \frac{360 - 75}{2} \\ \\ a + c = \frac{285}{2} \\ \\ therefore \: \: \: \: \: \: \: 2a =1 50 \\ \\ a = 75 \\ \\ c = \frac{285}{2} - \frac{75}{1} \\ \\ c = \frac{135}{2} .\end{gathered}

cot(a+b−c)=1

a+b−c=45...(i)

csc(b+c−a)=2

b+c−a=30...(ii)

solvingtheseweget

2b=75

b=

2

75

a−c=45−

2

75

a−c=

2

15

byanglesumproperty

a+b+c=180

a+c=180−

2

75

a+c=

2

360−75

a+c=

2

285

therefore2a=150

a=75

c=

2

285

−

1

75

c=

2

135

.