Question

solve (0°≤ Θ ≤90°)
math problem​

Answer 1

Answer:

x90

Step-by-step explanation:

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sin(x) + 2 = 3

sin(x) = 1

Answer 2

Answer:

90°

Step-by-step explanation:

cos2 θ – 3 cos θ + 2 = 2 sin2θ

If 0 < θ ≤ 90°

Put θ = 30°, 45°, 60° and 90° and satisfied the equation.

Put θ = 90°

⇒ 0 – 0 + 2 = 2 × 1

⇒ 2 = 2 (satisfied)

Detailed method:

cos2 θ – 3 cos θ + 2 = 2 sin2θ

⇒ cos2 θ – 3 cos θ + 2 = 2 (1 – cos2 θ)

⇒ cos2 θ – 3 cos θ + 2 = 2 – 2 cos2 θ

⇒ cos2 θ – 3 cos θ + 2 cos2θ = 2 – 2

⇒ 3 cos2 θ – 3 cos θ = 0

⇒ cos θ (cos θ – 1) = 0

Case 1 : If cos θ is 0 .

⇒ 3 cos θ = 0

⇒ cos θ = 0

⇒ cos θ = cos90°

θ = 90° or π / 2

Case 2 : If cos θ - 1 is zero.

⇒ cos θ - 1 = 0

⇒ cos θ = 1

⇒ cos θ = cos0°

But given that, θ is greater than 0°, cos θ ≠ cos0°

∴ The required measure of angle θ is 90°.

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