Question

Express sin 75º + cos 65º in terms of trigonometric ratios of angles between 0º and 45º.

Answer 1

Hi ,

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We know that ,

i ) Sin( 90 - A ) = cosA

ii ) Cos ( 90 - A ) = sinA

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Here ,

sin 75° + cos 65°

= sin ( 90 - 15 ) + cos ( 90 - 25 )

= cos 15° + sin 25°

I hope this helps you.

: )

Answer 2

sin75 + cos65




$\sin(75) + \cos(65)$


⏩ $sin ( 90 - 15 ) + cos ( 90 - 25 ) \: \: \: \: \: \: \: \: \: \: | \bold{sin ( 75 ) = sin ( 90 - 15 ) \: \: \: \: and \: \: \: \: cos ( 65 ) = cos ( 90 - 25 )}$


⏩ $cos( 15 ) + sin ( 25 ) \:\:\:\:\:\:\:\: | \bold{sin( 90 - \theta) = cos \theta \:\:\:\:\: and \:\:\:\: cos( 90 - \theta ) = sin \theta}$




Hence,

sin75 + cos25 = cos15 + sin25