solve
sin30.cos45+sin45.cos 30=
ChithaaMadanayake:
answer is becoming to decimals
I cant sure of my answer
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sin30°.cos 45° + sin 45°.Cos30°
==>1/2×1/√2+1/√2×√3/2
==>1+√3/2√2
==>2.2247. <==ans
Answered by
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you already know,
sin30° = 1/2 , cos30° = √3/2
cos45° = sin45° = 1/√2
so, sin30°. cos45° + sin45°. sin30°
= 1/2 × 1/√2 + 1/√2 × √3/2
= (1 + √3)/2√2
[ note : An important formula,
sin(A + B) = sinA.cosB + cosA.sinB
here, A = 30° and B = 45°
then, sin30° . cos45° + sin45° . cos30°
= sin(30° + 45°) [ from formula ]
= sin75°
hence, value of sin75° = (√3 + 1)/2√2 ]
sin30° = 1/2 , cos30° = √3/2
cos45° = sin45° = 1/√2
so, sin30°. cos45° + sin45°. sin30°
= 1/2 × 1/√2 + 1/√2 × √3/2
= (1 + √3)/2√2
[ note : An important formula,
sin(A + B) = sinA.cosB + cosA.sinB
here, A = 30° and B = 45°
then, sin30° . cos45° + sin45° . cos30°
= sin(30° + 45°) [ from formula ]
= sin75°
hence, value of sin75° = (√3 + 1)/2√2 ]
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