Question

cosec^4 theta-cot^4 theta/cosec^2 theta+cot^2 theta=?​

Answer 1

Answer :

1

Solution :

$\frac{cosec^{4}\:θ - cot^{4}\:θ}{cosec^{2}\:θ + cot^{2}\:θ }$

{cosec⁴θ - cot⁴θ}{cosec²θ - cot²θ}

{cosec⁴θ - cot⁴θ} × 1

(cosec²θ)² - (cot²θ)²

(cosec²θ + cot²θ)(cosec²θ - cot²θ )

$\frac{1}{cosec²\:θ - cot²\:θ}$(cosec² θ - cot² θ)

1

Note :

• cosec² θ - cot² θ = 1

• cosec² θ + cot²θ = $\frac{1}{cosec²\:θ - cot²\:θ}$

• a² - b² = (a + b)(a - b)