Question

prove that sin 20° cos 25° + cos 20 Sin 25=1/√2
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Answer 1

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$\longrightarrow \sf \sin20 \cos25 + \cos20 \sin25 = \frac{1}{ \sqrt{2} } \\ \\\longrightarrow \sf \sin(90 - 70) \cos25 + \cos(90 - 70) \sin25= \frac{1}{ \sqrt{2} } \\ \\ \longrightarrow \sf\cos70 \cos25 + \sin70 \sin25= \frac{1}{ \sqrt{2} } \\ \\\longrightarrow \sf \cos(70 - 25) = \frac{1}{ \sqrt{2} } \\ \\ \longrightarrow \sf\cos45= \frac{1}{ \sqrt{2} } \\ \\\longrightarrow \sf \frac{1}{ \sqrt{2} } = \frac{1}{ \sqrt{2} }$

LHS = RHS

Hence Proved

Answer 2

Step-by-step explanation:

=> sin 20 cos 25 + cos 20 sin 25 =1/√2

=> sin (90-70) = 25+cos (90-70) sin = 1/√2

=> cos 70 cos 25 + sin 70 sin 25 = 1/√2

=> cos (70-25) = 1/√2

=> cos= 45= 1/√2

=> 1/√2 = 1/√2

LHS = RHS.........proved.

this is your answer friends............ Salmønpanna

Hence