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Popular >

Reduce (cos(pi/2-x)^2)/( square root of 1-sin(x)^2)

Solution

simplify

\frac{( cos ^{2} ( \frac{π}{2 - x} ) )}{( 1 - sin ^{2} ( x ) )}

Solution

cos^{2} (\frac{π}{2 - x}) sec (x)

Solution steps

\frac{cos ^{2} ( \frac{π}{2 - x} )}{1 - sin ^{2} ( x )}

Use the Pythagorean identity:

1 = cos^{2} (x) + sin^{2} (x)

1 - sin^{2} (x) = cos^{2} (x)

= \frac{cos ^{2} ( \frac{π}{2 - x} )}{cos ^{2} ( x )}

cos^{2} (x) = cos (x)

= \frac{cos ^{2} ( \frac{π}{2 - x} )}{cos ( x )}

Use the basic trigonometric identity:

\frac{1}{cos ( x )} = sec (x)

= cos^{2} (\frac{π}{2 - x}) sec (x)

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\frac{( - 192 )}{( - 64 )}

Frequently Asked Questions (FAQ)

What is simplify ((cos^2(pi/(2-x))))/((sqrt(1-sin^2(x)))) ?
The solution to simplify ((cos^2(pi/(2-x))))/((sqrt(1-sin^2(x)))) is cos^2(pi/(2-x))sec(x)