Question

if 3sin (theta) +4 cos (theta) =5 then find the value of 4sin (theta) - 3cos (theta)​

Answer 1

Step-by-step explanation:

4sinθ+3cosθ =5 4sinθ =5−3cosθ.

Square (1), yields

16sin2θ=25−30cosθ+9cos2θ.

Use identity sin2θ=1−cos2θ and substitute to (2).

16(1−cos2θ) =25−30cosθ+9cos2θ 25cos2θ−30cosθ+9 =0 (5cosθ−3)2 =0 cosθ =

3

5

.

Consequently, sinθ=

4

5

. Thus,

4cosθ−3sinθ=4(

3

5

)−3(

4

5

)=0.

Answer 2

hope this helps you☺️☺️