Question

if tan theta=7/9 then solve (2-2cos theta)(3+cos theta )/(1-sin theta) (5+5sin theta)​

Answer 1

Correct Question :- if tan A = 7/9 , evaluate (2 - 2cosA)(3 + cos A) / (1 - sinA)(5 + 5sin A)

Solution :-

→ (2 - 2cosA)(3 + 3cos A) / (1 - sinA)(5 + 5sin A)

→ 2*3(1 - cosA)(1 + cosA) / 5(1 - sinA)(1 + sinA)

→ (6/5)[(1 - cosA)(1 + cosA) / (1 - sinA)(1 + sinA)]

using (a - b)(a + b) = a² - b²

→ (6/5)[(1 - cos²A)/(1 - sin²A)]

using :-

• 1 - cos²A = sin²A
• 1 - sin²A = cos²A

→ (6/5)[sin²A/cos²A]

using :-

• sinA / cosA = tanA

→ (6/5) * tan²A

putting value of tan A = (7/9) , we get,

→ (6/5) * (7/9)²

→ (6/5) * (49/81)

→ (2/5) * (49/27)

→ (98/135) (Ans.)

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