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If _1- _2=a and _1- _2=b, then

Question

If $sin θ_{1} - sin θ_{2} = a$ and $cos θ_{1} - cos θ_{2} = b$ , then

a^{2} + b^{2} \geq 4

a^{2} + b^{2} \leq 4

a^{2} + b^{2} \geq 3

a^{2} + b^{2} \leq 2

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Ava Discussed

sin θ_{1} - sin θ_{2} = a

and

cos θ_{1} - cos θ_{2} = b

, then

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Text solutionVerified

sin θ_{1} - sin θ_{2} = a ⟶ (1)

cos θ_{1} - cos θ_{2} = b ⟶ (2)

Squaring and adding (1) and (2)

a^{2} + b^{2} = 2 (1 - cos (θ_{1} - θ_{2}))

and,

- 1 < cos (θ_{1} - θ_{2}) < 1

Therefore,

0 \leq a^{2} + b^{2} \leq 4

Hence, option 'C' is correct.

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Question Text	If $sin θ_{1} - sin θ_{2} = a$ and $cos θ_{1} - cos θ_{2} = b$ , then
Answer Type	Text solution:1
Upvotes	150