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प्रश्न
In the following questions, two statements (i) and (ii) are given. Choose the valid statement.
(i) If `tan θ = 3/4`, then `cos θ = 3/5`
(ii) If sin θ = 3 cos θ, then `(sin θ - cos θ)/(sin θ + cos θ) = 1/2`
पर्याय
Only (i)
Only (ii)
Both (i) and (ii)
Neither (i) nor (ii)
MCQ
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उत्तर
Only (ii)
Explanation:
(i) False. `tan θ = "Opposite"/"Adjacent"`
= `3/4`
So, the triangle sides are 3, 4, 5.
Therefore, `cos θ = "Adjacent"/"Hypotenuse"`
= `4/5`, not `3/5`
(ii) True. If sin θ = 3 cos θ, write sin θ = 3c and cos θ = c (c ≠ 0).
Then `(sin θ - cos θ)/(sin θ + cos θ)`
= `(3c - c)/(3c + c)`
= `(2c)/(4c)` ...(Sign of c cancels)
= `1/2`
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