Question

Show that sin 32 degree.cos 58 degree + cos 32 degree. Sin58degree = 1

Answer 1

sin32°.cos58° + cos32°.sin58°

→ sin32°.cos(90-32) + cos32.sin(90-32)

[ sin∅ = cos(90-∅), cos∅=sin(90-∅))

→ sin32°.sin32° + cos32°.cos32°

→ sin²32° + cos²32°

→ 1

[sin²∅+cos²∅=1]

Hence Proved
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Answer 2

Hi ,

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We know the trigonometric identity

Sin² A + cos² A = 1

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LHS = sin32°cos58° + cos32°sin58°

=Sin32°cos(90-32)+cos32sin(90-58)

=sin32°sin32°+ cos32°cos32°

= sin² 32 + cos² 32°

= 1

= RHS

Or

SinAcosB + cosAsinB = sin( A + B )

Here ,

A = 32° , B = 58°

Sin32°cos58° + cos32°sin58°

= Sin( 32 + 58 )

= Sin90°

= 1

I hope this helps you.

:)