Question

if 16 cot A =12 then find sin A + cos A /sinA -cos A​

Answer 1

Given that,

16cot A = 12

We have to find the value of,

(sin A + cos A)/(sin A - cos A)

Dividing the numerator and denominator by sin A,

➠ [sin A + cos A]/sin A / [sin A - cos A]/sin A

We know that

• cos A / sin A = cot A

Thus,

➠ (1 + cot A)/(1 - cot A)

• It's given that : cot A = 12/16 = 3/4

➠ (1 + 3/4)/(1 - 3/4)

➠ (4 + 3/4)/(4 - 1)/4

➠ 7/4 × 4/1

➠ 7

Thus,

(sin A + cos A)/(sin A - cos A) = 7