Question

if cosecA=2 then find the value of cotA+sinA/1+cosA​

Answer 1

i hope my answer is right.

Answer 2

Given- CosecA=2

To find- (Cot A)+ {SinA/1+CosA}

Solution-

CosecA= Hypotenuse/Opposite= 2x/x              ⇒1

CosecA=1/SinA

2=1/SinA

Hence, SinA=1/2                                                 ⇒ 2

Using Pythagoras's Theorem Of Triangles

a² + b²= c²

Therefore,

x² + (BA)²= (2x)²

x²+BA²= 4x²

BA²= 3x²

BA=√3 x

Now,

Cot A= Adjacent/Opposite= √3 x/x = √3                       ⇒3

Cos A= Adjacent/Hypotenuse= √3 x/2x = √3/2           ⇒ 4

Therefore, According to the Question, we have to find,

(Cot A)+ {SinA/1+CosA}

Using the values of 2,3,4

⇒ √3 + [1/2 ÷ (1 + √3/2)]

⇒ √3 + [1/2 ÷ ( 2+ √3/2)]

⇒ √3 + [1/2 × 2/2+√3]

⇒ √3 + 1/2+√3

Taking L.C.M.

⇒(2+√3)(√3)/ 2+√3

⇒ 2√3+3/2+√3       ⇒ ANSWER