Question

please help me will mark as brainliest
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Answer 1

Answer:

Step-by-step explanation:

Given that,

3 cot θ - 4 = 0

cot θ = 4 / 3 = BC / AB ( ∵ In the right angle triangle ΔABC )

By using Pythagoras theorem,

AC² = AB²+ BC²

AC² = ( 3 )² + ( 4 )²

AC² = 9 + 16

AC² = 25

AC = ∛√25

AC = 5

sin θ = AB/ AC = 3/5 and cos θ = BC/ AC = 4/5.

∴ [ 3 sin θ + 4 cos θ ] / [ 3 sin θ - 2 cos θ ]

= [ ( 3 × 3/5 ) + ( 4 × 4/5 ) ] / [ ( 3 × 3/5 ) - ( 2 × 4/5 ) ]

= [ 9/5 + 16/5 ] / [ 9/5 - 8/5 ]

= [ 9+ 16 / 5 ] / [ 9 - 8 / 5 ]

= [ 25/5 ] / [ 1/5 ]

= 5 / ( 1/5)

= 5 × 5

= 25 is the answer.