What is 5/(sin^2(a))-5cot^2(a) ?

The solution to 5/(sin^2(a))-5cot^2(a) is 5

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simplify 5/(sin^2(a))-5cot^2(a)

simplify

\frac{5}{sin ^{2} ( a )} - 5 cot^{2} (a)

5

Solution steps

\frac{5}{sin ^{2} ( a )} - 5 cot^{2} (a)

Use the basic trigonometric identity:

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

= 5 csc^{2} (a) - 5 cot^{2} (a)

Use the Pythagorean identity:

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

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

= 5 \cdot 1

Factor out common term

5

= 5 (csc^{2} (a) - cot^{2} (a))

= 5

\frac{a}{2} + \frac{a ^{3}}{2} + \frac{a ^{5}}{2}

a^{3} b^{2} + a^{2} b^{3}

y^{5} - y^{3} - y^{2} + 1

9 p^{2} - 16 q^{2}

\frac{( 5 ^{n + 3} - 6 \cdot 5 ^{n + 1} )}{( 9 \cdot 5 ^{n} - 2 ^{2} \cdot 5 ^{n} )}