Question

31cos88/cos44*cos46 Cрооочно

Answer 1

31cos(90-2)/[1/2*(cos90+cos2)]=31sin2/[1/2(0+cos2)]=62sin2/cos2=62tg2

Answer 2

To simplify the expression 31cos(88)/cos(44)*cos(46), you can use trigonometric identities.

Recall the double-angle formula for cosine: cos(2θ) = 2cos^2(θ) - 1

Now, let's solve step by step:

1. Convert 88 degrees and 46 degrees to their double angle equivalents: 2 * 44 = 88 2 * 23 = 46

2. Apply the double-angle formula: cos(88) = 2cos^2(44) - 1 cos(46) = 2cos^2(23) - 1

3. Rearrange the equations to solve for cos^2(44) and cos^2(23): cos^2(44) = (cos(88) + 1) / 2 cos^2(23) = (cos(46) + 1) / 2

4. Substitute the expressions for cos(88) and cos(46): cos^2(44) = (2cos^2(44) - 1 + 1) / 2 cos^2(23) = (2cos^2(23) - 1 + 1) / 2

Simplify further: cos^2(44) = cos^2(44) cos^2(23) = cos^2(23)

Since the expressions are equal, we can cancel them out:

31 * cos(88) / cos(44) * cos(46) = 31 * 1 = 31

So, the simplified value of the expression is 31.