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Question
Find the most general value of θ satisfying the equation tan θ = –1 and cos θ = `1/sqrt(2)`.
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Solution
Given that: tan θ = –1 and cos θ = `1/sqrt(2)`
tanθ = –1
⇒ tan θ = `tan((-pi)/4)`
⇒ tan θ = `tan(2pi - pi/4)`
⇒ tan θ = `tan (7pi)/4`
∴ θ = `(7pi)/4`
Now cos θ = `1/sqrt(2)`
⇒ cos θ = `cos pi/4`
⇒ cos θ = `cos(2pi - pi/4)`
⇒ cos θ = `cos (7pi)/4`
∴ θ = `(7pi)/4` ........[tan θ and cos θ are positive in 4th quadrant]
Hence, the most general value of θ = `2"n"pi + (7pi)/4`.
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