What is 1/(sqrt(1-sin^2(a))) ?

The solution to 1/(sqrt(1-sin^2(a))) is sec(a)

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simplify 1/(sqrt(1-sin^2(a)))

simplify

\frac{1}{1 - sin ^{2} ( a )}

sec (a)

Solution steps

\frac{1}{1 - sin ^{2} ( a )}

Use the Pythagorean identity:

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

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

= \frac{1}{cos ^{2} ( a )}

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

= \frac{1}{cos ( a )}

Rewrite using trig identities

= sec (a)

cos (πn \cdot 2)

cos (arcsin (2 x))

36 - (6 (sin (θ)))^{2}

tan (- π + x)

cos (arctan (3 w))