Question

3
If x = 3 sin 0 + 4 cos 0 and y = 3 cos 0 - 4 sin 0 then prove that x2 + y2 = 25.
OR
A​

Answer 1

ɧɛƖƖơ ɱąɬɛ

Answer:

ɢɪᴠᴇɴ:

⇒x = 3 sin θ + 4 cos θ

⇒ y = 3 cos θ - 4 sin θ

ᴛᴏ ᴘʀᴏᴠᴇ :

x²+y²=25

ᴘʀᴏᴏF:

x²+y² =(3 sin θ + 4 cos θ )²  +  (3 cos θ - 4 sin θ )²

x²+y²= 9sin²θ+ 16cos²θ +2(3sinθ)(4cosθ)+9cos²θ+16sin²θ-2(3cosθ)( 4sinθ )

x²+y²=9sin²θ+ 16cos²θ+9cos²θ+16sin²θ

x²+y²=(9sin²θ+9cos²θ)+ (16cos²θ+16sin²θ)

x²+y²=9(sin²θ+cos²θ)+16(sin²θ+cos²θ)

x²+y²=9(1)+16(1)

x²+y²=9+16

x²+y²=25

ʜᴇɴᴄᴇ ᴘʀᴏᴏᴠᴇᴅ

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