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

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

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

simplify

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

1

Solution steps

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

Use the basic trigonometric identity:

\frac{1}{sin ( x )} = csc (x)

= csc^{2} (a) - \frac{1}{tan ^{2} ( a )}

Simplify

\frac{1}{tan ^{2} ( a )} : cot^{2} (a)

= csc^{2} (a) - cot^{2} (a)

Use the Pythagorean identity:

csc^{2} (x) = 1 + cot^{2} (x)

csc^{2} (x) - cot^{2} (x) = 1

= 1

(7 v - 9) - 2 (6 v + 9)

\frac{a ^{20}}{a ^{15}}

a - 1 x^{2} - 2 x + 1

(2 x^{5} y^{- 5})^{- 3}

2^{1 + l o g_{2} (n)}

What is 1/(sin^2(a))-1/(tan^2(a)) ?
The solution to 1/(sin^2(a))-1/(tan^2(a)) is 1