How to calculate the expression sin35*cos55+sin55*cos35?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find the value of sin 35*cos 55 + sin 55*cos 35.

Use the relation for sin(a+b) = sin a*cos b + cos a*sin b

sin 35*cos 55 + sin 55*cos 35

=> sin (35 + 55)

=> sin 90

=> 1

The value of sin 35*cos 55 + sin 55*cos 35 = 1.

Top Answer

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

This trigonometric sum returns the formula:

sin x*cos y + sin y*cos x = sin(x+y)

Let x = 35 and y = 55.

sin 35*cos 55 + sin 55*cos 35 = sin(35+55)

sin 35*cos 55 + sin 55*cos 35 = sin(90)

But sin 90 = 1, therefore the trigonometric sum yields 1.

We notice that we'll use trigonometric calculator, we'll get:

sin 55 = cos 35 = 0.8191...

sin 35 = cos 55 = 0.5735...

If we'll raise to square and then we'll add the values, we'll get also 1.

Therefore, the value of the trigonometric sum is sin 35*cos 55 + sin 55*cos 35 = 1.

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