Question

if cotA=17/18, then evaluate (1+sinA)(1-sinA)/(1+cosA)1-cosA)

Answer 1

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Answer 2

Answer:

(1+sinA)(1-sinA)/(1+cosA)1-cosA) = 289/324

Step-by-step explanation:

Given : If CotA = 17/18

To evaluate : (1+sinA)(1-sinA)/(1+cosA)1-cosA)

Solution :

(1 + SinA)(1 - SinA) / (1 + CosA)(1 - CosA)

= 1 - Sin^2 A / 1 - Cos^2 A

Since, (a + b)(a - b) = a^2 - b^2 (formula)

= Cos^2 A / Sin^2 A

Since, (Sin^2 A + Cos^2 A = 1) (formula)

= (CosA / SinA)^2

= (Cot)^2

Putting the value of given 'Cot A', we get

= (17/18)^2

= 289/324.

Therefore, Required result is

(1+sinA)(1-sinA)/(1+cosA)1-cosA) = 289/324