Question

if 4 cot theta is equals to 3 show that sin theta minus cos theta upon sin theta + cos theta is equals to one upon 7​

Answer 1

Given

• 4 cot Ф = 3

To prove

• (sin Ф - cos Ф) / (sin Ф + cos Ф) = 7

Explanation

• given that

⇨ 4 cot Ф = 3

⇨ cot Ф = 3 / 4

⇨ tan Ф = 4 / 3

• we need to prove

(sin Ф + cos Ф) / (sin Ф - cos Ф) = 7

⇨ LHS = (sin Ф + cos Ф) / (sin Ф - cos Ф)

dividing  both numerator and denominator by cos Ф

⇨ LHS = [(sin Ф + cos Ф)/cos Ф] / [(sin Ф - cos Ф)/cos Ф]

⇨ LHS = ( tan Ф + 1 ) / ( tan Ф - 1 )

substituting value of tan Ф

⇨ LHS = ( (4/3) + 1 ) / ( (4/3) - 1 )

⇨ LHS = ( (4+3)/3 ) / ( (4-3)/3 )

⇨ LHS = ( 7/3 ) / ( 1/3 )

⇨ LHS = ( 7/3 ) × ( 3 ) = 7 = RHS

Proved .