find the value sin20xcos70+cos20xsin70
Answers
Answered by
1
we know
sin(90-Ф)=cosФ
so...
sin20=cos70
so,
=sin20×cos70+cos20×sin70
=sin²20+cos²20
by pythagoras identity,
sin²+cos²=1
so
sin20×cos70+cos20×sin70=1
sin(90-Ф)=cosФ
so...
sin20=cos70
so,
=sin20×cos70+cos20×sin70
=sin²20+cos²20
by pythagoras identity,
sin²+cos²=1
so
sin20×cos70+cos20×sin70=1
Answered by
0
sin20*cos70+cos20*sin70 (let this be eq. 1)
cos(90-Ф)=sinФ
and
sin(90-Ф)=cosФ
substituting these in eq. 1,
sin20*cos(90-20)+cos20*sin(90-20)
=sin20*sin20+cos20*cos20
=sin²20+cos²20
taking 20=Ф
the eq. is
sin²Ф+cos²Ф
this is equal to 1
therefore answer is equal to 1
cos(90-Ф)=sinФ
and
sin(90-Ф)=cosФ
substituting these in eq. 1,
sin20*cos(90-20)+cos20*sin(90-20)
=sin20*sin20+cos20*cos20
=sin²20+cos²20
taking 20=Ф
the eq. is
sin²Ф+cos²Ф
this is equal to 1
therefore answer is equal to 1
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so sin 20 x cos 70 + cos 20 x sin 70 = sin(20+70) = sin 90 = 1