How can you simplify this sin²80+cos²50+cos²40+cos²100
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sin²80+cos²50-cos²40+cos²100= sin²80+cos²190
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Given that......sin²80+cos²50+cos²40+cos²100
=> sin²80+cos²50+cos²(90–50)+cos²(180–80)
=> sin²80+cos²50+[cos(90–50)]²+[cos(180–80)]²
As we know that,
cos(90–A) = sinA and cos(180–A) = –sinA.
then,
=> sin²80+cos²50+sin²50–sin²80
=> sin²50+cos²50
=> 1 { Because sin²A+cos²A = 1 }
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