Simplify 1 - sin 3-2 - - -sin -2 - - - 1 into a product-

1 + sin (3π2 α )sin (π2 + α ) 1 ⇒sin (π2 + α ) 1 + sin (3π2 α )sinπ2cosα + sinαcosπ2 1 ⇒cosα 1 + sin3π2cosα sinαcos3π2cosα 1 ...

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Theorems on Integration

Simplify 1 ...

Question

Simplify $1 + \frac{sin (\frac{3 π}{2} - α)}{sin (\frac{π}{2} + α) - 1}$ into a product.

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Solution

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{[1 - sin (π + α) + cos (π + α)]}^{2} + {[1 - sin (\frac{3 π}{2} + α) + cos (\frac{3 π}{2} - α)]}^{2} = a + b sin 2 α

a

b

\frac{s i n (π - α)}{s i n α - c o s α t a n \frac{α}{2}} + c o s (π - α) = 1.

s i n^{2} 0 + s i n^{2} \frac{π}{6} + s i n^{3} \frac{π}{3} + s i n \frac{π}{2}

(\frac{1}{{sec}^{2} α - {cos}^{2} α} + \frac{1}{{csc}^{2} α - {sin}^{2} α}) {cos}^{2} α . {sin}^{2} α = \frac{1 - {cos}^{2} α . {sin}^{2} α}{2 + {cos}^{2} α . {sin}^{2} α}

α + 4, α - \frac{7}{2}, α - \frac{5}{2}, α - 3, α - 2, α + \frac{1}{2}, α - \frac{1}{2}, α + 5 (α > 0)

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