Question

if 3 sin theta + 4 cos theta = 5 then the value of 4sintheta - 3 cos theta​

Answer 1

Step-by-step explanation:

3sin+4cos=5

on sq. both side

(3sin+4cos)²=5²

9sin²+24sin•cos+16cos²= 25 eq.1

let 4sin-3cos=x

on sqaureing both side

(4sin-3cos)²=x²

16sin²-24sin•cos+9cos²=x². eq.2

on adding both eq we get

16sin²+9sin²+16cos²+9cos²+24sincos-24sincos= x²+25

25sin²+25cos²=x²+25

25(sin²+cos²)=x²+25

25×1=x²+25

25=x²+25

0=x²

0=x

hence 4sin-3cos is equal to 0

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