Question

I if cotQ=7/8, evaluate
(1+sinQ)(1-sinQ)/(1+cosQ)(1-cosQ)

Answer 1

Given :-

• cotQ = 7/8 .

To Find :-

• (1+sinQ)(1-sinQ)/(1+cosQ)(1-cosQ)

Solution :-

→ (1+sinQ)(1-sinQ)/(1+cosQ)(1-cosQ)

using (a+b)(a-b) = (a² - b²) in Numerator & Denominator we get,

→ ( 1 - sin²Q) / ( 1 - cos²Q)

Now, we know That,

• sin²A + cos²A = 1 or,
• sin²A = 1 - cos²A or,
• cos²A = 1 - sin²A

So,

→ (cos²Q) / (sin²Q)

→ (cosQ/sinQ)²

Now, using (cosA / sinA) = cotA , we get ,

→ (cotQ)²

→ (7/8)²

→ (49/64) (Ans).

Answer 2

Answer:-

Cot Q = 7/8

=> Cot² Q = (7/8)²

=> Cot² Q = 49/64

(1 + Sin Q)(1 - Sin Q)/(1 + Cos Q)(1 - Cos Q)

=> (1 - Sin² Q)/(1 - Cos² Q)

[ (a + b)(a - b) = a² - b² & 1² = 1]

=> Cos² Q/Sin² Q

[ Sin² A + Cos² A = 1 => Sin² A = 1 - Cos² A and Cos² A = 1 - Sin² A]

=> Cot² Q

[ Cos² A/Sin² A = Cot² A]

=> 49/64