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Question
`If sin theta = cos( theta - 45° ),where theta " is acute, find the value of "theta` .
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Solution
𝑊𝑒 ℎ𝑎𝑣𝑒,
Sin 𝜃 = cos(𝜃 − 45°)
⟹ cos(90° − 𝜃) = cos(𝜃 − 45°)
Comparing both sides, we get
` 90° - theta = theta - 45°`
` ⇒ theta + theta = 90° + a=45°`
`⇒ 2 theta = 135°`
`⇒ theta = ((135)/2)^°`
∴ 𝜃 = 67.5°
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