Question

If 3 sin theta + 5 cos theta is equal to 5 then prove that 5 sin theta minus 3 cos theta is equal to 3hat 5 sin theta minus 3 cos theta is equal

Answer 1

Question :-

→ If ( 3sin θ + 5 cos θ ) = 5 , prove that ( 5 sin θ - 3 sin θ ) = ± 3 .

Answer :-

We have ,

→ ( 3 sin θ + 5cos θ )² + ( 5 sinθ - 3 cos θ )² .

= 9( sin²θ + cos²θ ) + 25( sin²θ + cos²θ ) .

= ( 9 + 25 ) .

= 34 .

∴ ( 3 sin θ + 5 sin θ )² + ( 5 sin θ - 3 cos θ )² = 34 .

⇒ 5² + ( 5 sin θ - 3 cos θ )² = 34 . [ ∵ 3 sin θ + 5 cos θ = 5 ]

⇒ 25 + ( 5 sin θ - 3 cos θ )² = 34 .

⇒ ( 5 sin θ - 3 cos θ )² = 34 - 25 .

⇒ ( 5 sin θ - 3 cos θ )² = 9 .

⇒ ( 5 sin θ - 3 cos θ ) = ±√9 .

⇒ ( 5 sin θ - 3 cos θ ) = ± 3 .

Hence, ( 5 sin θ - 3 cos θ ) = ± 3 .

Answer 2

Step-by-step explanation:

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