Verified Answer :

For 0 < x < 90

cos (90-x) = sin (x), 

and
sin (90-x) = cos(x)


Let's just try and pick the top one, the equation will become

cos (90-40) = sin (40)

Cos (50) = sin (40)


Hope this helps

carlos2112

Answer:

\(x\approx0.6427876097\)

Explanation:

Solve for x:

\(cos(x)=sin(40)\\\\0

Rewrite the right hand side using the following identity:

\(sin(\theta)=cos(\theta - \frac{\pi}{2} )=cos( \theta- 90)\)

Therefore:

\(cos(x)=cos(40-90)=cos(-50)\)

Since cosine function is an even function:

\(cos(-\theta) =cos(\theta)\)

Hence:

\(cos(-50)=cos(50)\)

\(cos(x)=cos(50)\)

Finally, take the inverse cosine of both sides:

\(x\approx0.6427876097\)

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