Question

prove that 1+cot square theta/1+cosectheta=cosec theta

Answer 1

Answer:

$1+\frac{cot^{2}\theta}{1+cosec\theta}=cosec\theta$

Step-by-step explanation:

$LHS = 1+\frac{cot^{2}\theta}{1+cosec\theta}$

$=1+\frac{cosec^{2}\theta-1}{cosec\theta+1}$

/* we know the Trigonometric identity:

cot²A = cosec²A-1 */

$=1+\frac{(cosec\theta+1)(cosec\theta-1)}{(cosec\theta+1)}$

/*By algebraic identity:

a²-b² = (a+b)(a-b) */

$=1+cosec\theta-1\\=cosec\theta\\=RHS$

$1+\frac{cot^{2}\theta}{1+cosec\theta}=cosec\theta$

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Answer 2

Answer :

Hey mate...

Please refer to the attachment.

Hope it helps you you mate...