Question

without using calculator prove that sin420 cos390 +cos(-300)sin(-330)=1​

Answer 1

Answer:

no it is 0.5

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Answer 2

Answer:

$sin(420) = sin(90 × 4 + 60) = sin60 = \frac{ \sqrt{3} }{2}$

$cos(390) = cos(90 × 4 + 30) = cos30 = \frac{ \sqrt{3} }{2}$

$cos(- 300) = cos(300) = cos(90 ×3 + 30) = sin30 = \frac{1}{2}$

$sin(- 330) = - sin(330) = - sin(90 ×3 + 60) = cos60 = \frac{1}{2}$

LHS now become

$\frac{ \sqrt{3} }{2} \times \frac{ \sqrt{3} }{2} + \frac{1}{2} \times \frac{1}{2} \\ = \frac{3}{4} + \frac{1}{4} \\ = \frac{3 + 1}{4} \\ = \frac{4}{4} \\ = 1$