cotA =5/12 find (1+sinA) (1-sinA)/(1+cosA) (1-cosA)
Answers
Answered by
0
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:
Answered by
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
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