Question

sin²200 + sin²250° + sin² 280° + sin²370°​

Answer 1

Answer:

Hey mate !

The answer for this question is 2

Step-by-step explanation:

Let's start solving the problem,

= sin²200 + sin²250° + sin² 280° + sin²370°​

= sin²(180+20) + sin²(180+70) + sin²(360-80) + sin²(360+10)

= (-sin20)² + (-sin70)² + (-sin80)² + (sin10)²

= sin²20 + sin²70 + sin²80 + sin²10

= sin²(90-20) + sin²70 + sin²(90-10) + sin²10

= (cos²70 + sin²70) + (cos²10 + sin²10)

From sin²x + cos²x = 1 property we get,

= 1 + 1

= 2

Notes: 1. sin(180+x) = -sin(x)

           2. sin(360-x) = -sin(x)

           3. sin(360+x) = sin(x)

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