Question

cotA =5/12 find (1+sinA) (1-sinA)/(1+cosA) (1-cosA)​

Answer 1

Answer:

sin

A

+

cos

A

=

17

13

 

Explanation:

cot

A

=

5

12

cotangent= adjecent/opposite

thus the hypotenuse is:

h

=

√

25

+

144

=

13

sin

A

=

12

13

cos

A

=

5

13

sin

A

+

cos

A

=

12

13

+

5

13

=

17

13

Step-by-step explanation:

Answer 2

Given

⇒CotA = 5/12

To Find

⇒{(1+SinA)(1-SinA)}/{(1+CosA)(1 - CosA)}

First of all Simplify The equation

⇒{(1+SinA)(1-SinA)}/{(1+CosA)(1 - CosA)}

Using this identity

⇒(a - b)(a + b) = a² - b²

We get

⇒(1 - Sin²A)/(1 - Cos²A)

We Know that

⇒Sin²A + Cos²A = 1

⇒Cos²A = 1 - Sin²A

⇒Sin²A = 1 - Cos²A

We  get

⇒(1 - Sin²A)/(1 - Cos²A)

⇒Cos²A/Sin²A = Cot²A

We have CotA = 5/12

⇒Then, Cot²A = (5/12)²

⇒Cot²A = 25/144

Answer

⇒{(1+SinA)(1-SinA)}/{(1+CosA)(1 - CosA)} = 25/144